"A grain of discovery"

[Dictated into a smart phone. I tried to catch all of the homonyms, but, hell, it's late and I'm fading.]

Having opened up what will probably be a long thread on Common Core, we really need to bring George Pólya into the conversation.

Pólya was a first rate mathematician and an enthusiastic and dedicated teacher. so dedicated that he spent somewhere in the neighborhood of 70 years in front of a classroom and he spent a large part of those years thinking long and hard about how we learn mathematics.

I'll go into more detail later about his conclusions. In addition to being insightful and interesting in their own right, they provide a useful alternative when discussing both the rigorously axiomatic approach of 'new math' and the reductionist 'deliberate practice' being pushed by advocates of common core.

For now though, I think it's important to start with the underlying assumptions of Pólya's approach to mathematics: Humans are by nature curious and drawn to interesting problems; therefore, if taught correctly, math should be both stimulating and enjoyable (as are the many popular games and puzzles based on mathematics).

In other words, if my kids hate math, I'm not teaching it right.

This is how Pólya opens the preface to How to Solve It:

A great discovery solves a great problem but there is a grain of discovery in the solution of any problem. Your problem may be modest; but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery. Such experiences at a susceptible age may create a taste for mental work and leave their imprint on mind and character for a lifetime.

Thus, a teacher of mathematics has a great opportunity. lf he fills his allotted time with drilling his students in routine operations he kills their interest, hampers their intellectual development, and misuses his opportunity. But if he challenges the curiosity of his students by setting them problems proportionate to their knowledge, and helps them to solve their problems with stimulating questions, he may give them a taste for, and some means of, independent thinking. 

Here's the entire preface, preprefaced with more of my thoughts on the subject.

Diane Ravitch provides some historical perspective on international math rankings

A perverse problem with education reform is that, on a high enough level, almost everyone agrees it's a good thing. Unfortunately, it is easy to confuse the question of "is it a good idea to improve education?" with some far murkier questions such as: 

Why is it urgent now to change education radically?

What constitutes ideal educational outcomes?

What are the most effective steps for improving education?

These are difficult questions which interact with each other in highly complex ways. Discussing them is hard enough under the best conditions but it gets much worse when advocates for certain proposals dismiss criticism by saying the people on the other side simply don't care about children (a practice that far predates the current education reform debate).

As for the question of urgency, members of the education reform movement have almost always pointed to either our decline in international tests such as PISA or our race and class based achievement gaps. The second of these is very real and very worrisome, but it often has a rather indirect relationship with reform proposals like introducing common core or greatly reducing teacher tenure.

As for the first, education historian and movement reformer turned gadfly, Diane Ravitch offers the following context.

International testing began in the mid-1960s with a test of mathematics. The First International Mathematics Study tested 13-year-olds and high-school seniors in 12 nations. American 13-year-olds scored significantly lower than students in nine other countries and ahead of students in only one. On a test given only to students currently enrolled in a math class, the U.S. students scored last, behind those in the 11 other nations. On a test given to seniors not currently enrolled in a math class, the U.S. students again scored last.

The First International Science Study was given in the late 1960s and early 1970s to 10-year-olds, 14-year-olds, and seniors. The 10-year-olds did well, scoring behind only the Japanese; the 14-year-olds were about average. Among students in the senior year of high school, Americans scored last of eleven school systems.

In the Second International Mathematics Study (1981-82), students in 15 systems were tested. The students were 13-year-olds and seniors. The younger group of U.S. students placed at or near the median on most tests. The American seniors placed at or near the bottom on almost every test. The “average Japanese students achieved higher than the top 5% of the U.S. students in college preparatory mathematics” and “the algebra achievement of our most able students (the top 1%) was lower than that of the top 1% of any other country.” (The quote is from Curtis C. McKnight and others, The Underachieving Curriculum: Assessing U.S. Mathematics from an International Perspective, pp. 17, 26-27). I summarized the international assessments from the mid-1960s to the early 1990s in a book called National Standards in American Education: A Citizen’s Guide (Brookings, 1995).

The point worth noting here is that U.S. students have never been top performers on the international tests. We are doing about the same now on PISA as we have done for the past half century.

Does it matter?

In my recent book, Reign of Error, I quote extensively from a brilliant article by Keith Baker, called “Are International Tests Worth Anything?,” which was published by Phi Delta Kappan in October 2007. Baker, who worked for many years as a researcher at the U.S. Department of Education, had the ingenious idea to investigate what happened to the 12 nations that took the First International Mathematics test in 1964. He looked at the per capita gross domestic product of those nations and found that “the higher a nation’s test score 40 years ago, the worse its economic performance on this measure of national wealth–the opposite of what the Chicken Littles raising the alarm over the poor test scores of U.S. children claimed would happen.” He found no relationship between a nation’s economic productivity and its test scores. Nor did the test scores bear any relationship to quality of life or democratic institutions. And when it came to creativity, the U.S. “clobbered the world,” with more patents per million people than any other nation.

Baker wrote that a certain level of educational achievement may be “a platform for launching national success, but once that platform is reached, other factors become more important than further gains in test scores. Indeed, once the platform is reached, it may be bad policy to pursue further gains in test scores because focusing on the scores diverts attention, effort, and resources away from other factors that are more important determinants of national success.” What has mattered most for the economic, cultural, and technological success of the U.S., he says, is a certain “spirit,” which he defines as “ambition, inquisitiveness, independence, and perhaps most important, the absence of a fixation on testing and test scores.”

Baker’s conclusion was that “standings in the league tables of international tests are worthless.”

Fairness and regulation

Dean Baker has some good points:

For the last three decades the government has pursued a wide range of policies that have had the effect of redistributing income upward. For example our trade policy, by deliberately placing manufacturing workers in direct competition with low paid workers in the developing world, has lowered the wages of large segments of the work force. By contrast, we have left in place the restrictions that protect doctors and other highly paid professionals from foreign competition, ensuring that their pay stays high.

and

The question at issue is not the amount of redistribution, the question is the direction of the redistribution. The Post seems to want readers to imagine that the upward redistribution of the last three decades was just a fact of nature, as opposed to being an outcome of government policy. That is a major distortion of reality.

This really is the heart of the argument about inequality today.  The notion that the wages earned by high status professions (medicine, finance) is a result of pure market forces and nothing to do with the regulatory environment is weak.  In the same sense, the huge returns to intellectual property have a lot to do how the laws protecting this property are implemented.  And it is not an accident that 401(k) style retirement plans are popular among companies that get to collect management fees.  This isn't to say all IP law is bad (it isn't) or all wages earned by finance gurus is unearned (also untrue). 

But it is a worthwhile starting point to realize that the web of laws and customs that we do have does benefit some groups at the expense of others.  So it is a very weak claim to argue fairness of economic outcomes in the face of differential regulatory treatment. 

Happy PISA Day, everybody!

Richard Rothstein and Martin Carnoy of the Economic Policy Institute have some strong words about how PISA data is released.

It is usual practice for research organizations (and in some cases, the government) to provide advance copies of their reports to objective journalists. That way, journalists have an opportunity to review the data and can write about them in a more informed fashion. Sometimes, journalists are permitted to share this embargoed information with diverse experts who can help the journalists understand possibly alternative interpretations.

In this case, however, the OECD and ED have instead given their PISA report to selected advocacy groups that can be counted on, for the most part, to echo official interpretations and participate as a chorus in the official release.* These are groups whose interpretation of the data has typically been aligned with that of the OECD and ED—that American schools are in decline and that international test scores portend an economic disaster for the United States, unless the school reform programs favored by the administration are followed.

The Department’s co-optation of these organizations in its official release is not an attempt to inform but rather to manipulate public opinion. Those with different interpretations of international test scores will see the reports only after the headlines have become history.

Such manipulation in the release of official government data would never be tolerated in fields where official data are taken seriously. Can you imagine the Census Bureau providing its poverty data in advance only to advocacy groups that supported the administration, and then releasing its report to the public at an event at which these advocacy groups were given slots on a program to praise the administration’s anti-poverty efforts? What if the Bureau of Labor Statistics gave its monthly unemployment report in advance to Democrats, but not to Republicans, and then invited Democratic congressional leaders to participate in the official release?

I know I've hammered this point before, but the education reform movement has been playing a very aggressive long game when it comes to lobbying and PR. Add to that a tradition of advocate research and a culture that tends to eschew firewalls and turn a blind eye to conflicts of interest, then lubricate the gears with a flood of government contracts and private grants. The result is a movement prone to all manner of problems and abuses.

The problem isn't that most of the people in the movement are uncaring and insincere; it's that they aren't. The typical movement reformer cares deeply about kids and genuinely feels that our education system is in a state of crisis. Given that mindset, it's easy to understand the decision to feed the data to groups that will give it the 'correct' interpretation in those first few days when the narrative starts to set.

But to understand the behavior is one thing. To condone it is another. Official data needs to be presented so that all sides start on an equal footing, even if that means your side may lose.

* The Alliance for Excellent Education, Achieve, ACT, America Achieves, the Asia Society, the Business Roundtable, the Council of Chief State School Officers, the College Board, the National Board for Professional Teaching Standards, and the National Center on Education and the Economy.

"Up until about a month ago, we all knew what merit pay meant."

Dana Goldstein has a good write-up on a recent education study:

In 10 cities, including Los Angeles, Miami, and Houston, researchers at Mathematica identified open positions in high-poverty schools with low test scores, where kids performed at just around the 30th percentile in both reading and math. To fill some of those positions, they selected from a special group of transfer teachers, all of whom had top 20 percent track records of improving student achievement at lower poverty schools within the districts, and had applied to earn $20,000 to switch jobs. The rest of the open positions were filled through the usual processes, in which principals select candidates from a regular applicant pool.

If a transfer teacher stayed in her new, tougher placement for two years, she’d earn the $20,000 in five installments, regardless of how well her new students performed. In public education, $20,000 is a whopping sum, far more generous than the typical merit pay bonus of a few hundred or a few thousand dollars.

In the process, a remarkable thing happened. The transfer teachers significantly outperformed control-group teachers in the elementary grades, raising student achievement by 4 to 10 percentile points—a big improvement in the world of education policy, where infinitesimal increases are often celebrated.

 but I have one big problem with the way she presents the findings.

That’s why the results of a new study, the Talent Transfer Initiative, financed by the federal government, are so important. Surprisingly, this experiment found merit pay can work.

Up until about a month ago, we all knew what merit pay meant. Under these systems of compensation, your pay would vary based on certain performance metrics from the previous period.

The initial rationale for applying this type of compensation to education was based on the assumption that teachers would work harder and do a better job if their performance (defined by their students' test scores) was tied to their pay . This played in very closely with the sub-narrative that problems in American education were largely driven by lazy, tenured teachers.

Unfortunately, when this idea was was tried in various pilot programs, it failed to show any substantial effect. It almost appeared as if teachers were already, for the most part, trying to do their best even when their pay didn't vary with performance.

This failure of concept led to a wave of revisionism from movement reformers such as Jonathan Chait. They quickly came up with a new claim. Under the revised history, rationale for merit pay had never been about incentives; push had always been about selection and retention of the best people.

There were always significant problems with this new rationale. Unless you were to assume that being a good teacher was strongly correlated with being bad at mathematics, the size of the bonuses would have to be very large to compensate for the deferment and variability of compensation. Even more troubling, the metrics proposed to evaluate teachers had been shown to be wildly unstable, thus teachers would have very little idea of what their annual take-home pay would be from year-to-year.

The flaws in that second rationale were so obvious, it almost suggested that the proponents were simply looking for a face-saving claim to make before backing away from the issue.

That face-saving quality is even more prominent in the coverage of the recent Chicago experiment in hiring bonuses for teachers. As generally presented by Goldstein and others, this seems like a partial win for both sides. Movement reformers can point to the findings and say that merit pay works while counter-reform advocates can point out that the teachers who got these great results were highly experienced and certified.

The problem with that story is that the first part of the claim is based on a complete 180-degree redefinition of merit pay. The bonus had nothing to do with metrics of success; instead it was solely contingent on those teachers serving out a specified term in the position. In other words, it used the exact same rationale that movement reformers have always objected to when applied to tenure and pay raises for seniority. (You can see Diane Ravitch making some of the same points here.)

I understand the benefits of keeping a debate civil. We should constantly make it clear that the vast majority of people on both sides of this debate share the common goal of improving education. We cannot, however, let the desire for civility become an excuse for dishonesty, particularly not when we are reporting on research that affects open policy questions.

This study suggest taking something like the Canadian approach to managing and compensating teachers. In other words, roughly the opposite of what those advocating merit pay have called for. You can question the quality of this study. You can call it impractical and question whether the results can be scaled up to a useful level. What you cannot do is claim that the data supports your position because you have changed your definitions mid-argument.

Weekend blogging -- save this one for late in the day

As a former creative writing major, I probably shouldn't admit this but I wasn't really familiar with Paul Verlaine and I had no idea that Clair de lune was inspired by his poem of the same name.

Nothing more to add in the way of comment except the recommendation that you wait till late in the evening before pushing play.




Clair de Lune by Paul Verlaine

Your soul is a chosen landscape
Where charming masqueraders and bergamaskers go
Playing the lute and dancing and almost
Sad beneath their fanciful disguises.

All sing in a minor key
Of victorious love and the opportune life,
They do not seem to believe in their happiness
And their song mingles with the moonlight,

With the still moonlight, sad and beautiful,
That sets the birds dreaming in the trees
And the fountains sobbing in ecstasy,
The tall slender fountains among marble statues.

Putting Arne Duncan's remarks in context

“It’s fascinating to me that some of the pushback is coming from, sort of, white suburban moms who — all of a sudden — their child isn’t as brilliant as they thought they were and their school isn’t quite as good as they thought they were, and that’s pretty scary,” Arne Duncan said. “You’ve bet your house and where you live and everything on, ‘My child’s going to be prepared.’ That can be a punch in the gut.”

To understand why Duncan hit such a nerve, you need to consider the long and complicated role that racial politics have played in this debate.

The public face of the education reform movement has always been pictures of eager young African-American and Hispanic children. Not only has the movement been sold as a way of helping these children but people who object to parts of the reform agenda have often been accused, implicitly or explicitly, of not wanting to help children of color. This naturally has caused some resentment by those, such as myself, who disagree with many of the proposals and who have actually taught in places like Watts and the Mississippi Delta, but there are more serious sources of tension.

For starters, with certain notable exceptions, the leaders of the reform movement tend to be white or Asian (for example, "2012 members of TFA are 62 percent white and only 13 percent African American"). By comparison, the tenured and/or unionized teachers who have paid the highest price in terms of policy changes and school closures have been disproportionately African-American. Under these circumstances, you can imagine the reaction when education reformers make statements like “I think the best thing that happened to the education system in New Orleans was Hurricane Katrina.”


(as a side note, Jay Altman is one of the best paid administrators in the city)

Even more troubling is the disconnect between the marketing and the actual focus of the reform movement. Though the defining image of the movement is of a reformer surrounded by a happy group of African-American or Hispanic elementary school students in brand-new charter school uniforms, almost none of the major reform initiatives are specifically targeted at helping these particular kids. Initiatives like Common Core and teacher accountability are being proposed for all schools. Sometimes reformers will argue that though these changes affect all students they will have their greatest impact on disadvantaged kids. Other times, they simply let their photo ops do the talking for them.

Even TFA, which was held up as the definitive program for helping kids in poor neighborhoods, is now focusing more on developing leaders and administrators and is actually providing teachers for areas like Chicago and even more notably Huntsville that have a surplus of highly qualified instructors applying for the jobs.

Perhaps people did read too much into Duncan's comments but, considering recent history, you can see how some might react badly to his suggestion that race was a factor in people's decision to criticize his proposals.

So what am I missing?

This conclusion of a piece by Megan McArdle was confusing:

Those victims should not be abandoned -- no American should be allowed to starve in retirement. But the federal government should not step in to guarantee those false promises, any more than it should attempt to re-create the vulnerable housing developments that were washed away by the storm.

The context is that of the Detroit bankruptcy, where retirees are getting 16 cents on the dollar.  There is also issues with health care that I am not clear about, but I am presuming that these people are eligible for Medicare (they are not eligible for Social Security since they did not participate in the contributions).

What I don't understand is what the path forward being proposed is?  We cannot recover the money from past administrations, and the issues with the pension are complex.  Fault is very hard to assess.  So the choices seem to be: short other creditors, default on pension obligations, or find another source of funds.  Unless the suggestion is that the state should backstop these obligations, I am unclear what the source might be? 

I am hoping that further information makes this situation seem less dire. 

"As God as my witness..." is my second favorite Thanksgiving episode line

If you watch this and you could swear you remember Johnny and Mr. Carlson discussing Pink Floyd, you're not imagining things. Hulu uses the DVD edit which cuts out almost all of the copyrighted music. .

As for my favorite line, it comes from the Buffy episode "Pangs" and it requires a bit of a set up (which is a pain because it makes it next to impossible to work into a conversation).

Buffy's luckless friend Xander had accidentally violated a native American grave yard and, in addition to freeing a vengeful spirit, was been cursed with all of the diseases Europeans brought to the Americas.

Spike: I just can't take all this mamby-pamby boo-hooing about the bloody Indians.
Willow: Uh, the preferred term is...
Spike: You won. All right? You came in and you killed them and you took their land. That's what conquering nations do. It's what Caesar did, and he's not goin' around saying, "I came, I conquered, I felt really bad about it." The history of the world is not people making friends. You had better weapons, and you massacred them. End of story.
Buffy: Well, I think the Spaniards actually did a lot of - Not that I don't like Spaniards.
Spike: Listen to you. How you gonna fight anyone with that attitude?
Willow: We don't wanna fight anyone.
Buffy: I just wanna have Thanksgiving.
Spike: Heh heh. Yeah... Good luck.
Willow: Well, if we could talk to him...
Spike: You exterminated his race. What could you possibly say that would make him feel better? It's kill or be killed here. Take your bloody pick.
Xander: Maybe it's the syphilis talking, but, some of that made sense.

Equality and Adam Smith

Bill Gardner from the Incidental Economist (in comments):

As you know, Adam Smith was a moral philosopher. You might want to ponder this quote from the Wealth of Nations:

“No society can surely be flourishing and happy, of which the far greater part of the members are poor and miserable. It is but equity, besides, that they who feed, clothe, and lodge the whole body of the people, should have such a share of the produce of their own labour as to be themselves tolerably well fed, clothed, and lodged.”

I think that this really is the piece that modern objectivists (Randians) miss.  Even in Atlas Shrugged, the hyper-capitalist society was clearly defined as being better for the average worker.  In fact, the story of the company becoming socialist suggested that socialism under-mined values like generosity. 

The notion that an equitable society is a better society is very important and yet seems to be increasingly lost in the rhetoric.  When we have a high unemployment rate, it cannot merely be laziness that prevents work and it seems that we are having trouble with the most expensive part of the formulation (lodged --it is housing that is the big expense these days). 

Now before the argument that this inequality was necessary for progress comes into being, remember that Adam Smith celebrated a nation of shopkeepers, not of corporations. 

Teacher incentives

Dana Goldstein writes about a program that gives a $20,000 bonus to teachers who transfer to "high poverty, low test score" schools.  These are all established mid-career teachers, not ivy-leaguers parachuted in to help.  They showed benefit in elementary schools but not middle school.  All of these transfers were inter-urban.

I have two thoughts.  One, huge merit pay bonuses are the precise opposite of revenue neutral.  There is no evidence that cutting everyone's pay to afford these bonuses for some teachers would be a cost-effective strategy.  Its an average causal effect applied to a population already getting an underlying rate of compensation.  So what this really has to be judged against are other interventions that would spend the same money in different ways. 

Two, the political feasibility seems low.  So long as education is funded via local taxes, it seems challenging to build support for a program to pull good teachers out of well funded schools and push them into high poverty area schools (almost certainly with lower funding).  Just how one might build the political coalition to do this (without encouraging mass abandonment of existing public schools) seems to be a open question.

You will never guess who I'm quoting...

And, God help me, she pretty much nails it:

There’s much more to the fight than simple left-right divisions. The Common Core peddlers include meddling, Fed Ed Republicans from Jeb Bush and Mike Huckabee to progressive billionaires Bill and Melinda Gates to Newscorp. media giant Rupert Murdoch and dozens of educational corporate special interests that stand to gain billions from the Common Core testing/textbook/data-mining boondoggle.

I have to give credit where credit is due, even if it costs us at least one loyal reader.

Education blogging -- Common Core, accountability and the cost of deadwood

I've started digging into the Common Core standards and one of the things that hit me was the large amount of what I would consider deadwood, topics of limited value that take up valuable class time (my favorite example is synthetic division, but there are plenty of others).

The damage caused by deadwood is not that great when teachers are allowed some leeway in deciding what to focus on, but in an age of standardized tests and fetishized accountability, teachers are forced to make difficult decisions. Math teacher Gary Rubinstein has a truly depressing example.

When teachers have to teach too many topics, they do not have time to cover them all in a deep way.  The teacher, then, has to choose which topics to cover in a meaningful way, and which to cover superficially.  It would be as if an English teacher was told to cover fifty novels with her class.  Not being able to have her classes read all fifty books, she would pick some to read fully while having her class read excerpts or even summaries of the other ones.

I got to witness an extreme example of this decision making when I graded the Geometry Regents at the centralized grading center this past June.  A huge part of Geometry, in my mind the most important part, is deductive proofs.  I’d say that over half of a ‘true’ Geometry course would involve proving different theorems.  Well, on the Geometry Regents these proofs are not a large percent of the test, less than ten points out of eighty.  So on the June Regents the last question on the test, a six point question, was the proof question and I was assigned to grade about 200 papers from a school, I won’t say which one, to grade.  As I graded I noticed that many of the students left the proof blank.  By the end of my grading I realized that out of 200 papers, all that could have received up to 6 points for the proof — a total of 1,200 potential points to have been earned on this question, I had awarded only two points total.  That’s two points out of a possible 1,200.  I asked around and the consensus was that teachers, knowing that proofs would take months to cover but be only worth less ten percent of the points on the test, would be too risky to teach.  All the time spent on this tough topic would only, at best, get the students a few extra points while they would lose all that time they could use to teach some of the easier topics that were more likely to be on the test.

Of course, we could have a long discussion on whether proofs belong in HS math classes (I tend to agree with Rubinstein on this one, at least when it comes to geometry), but it's important to realize that's not what happened here. There was no discussion. No arguments were made. No supporting data was gathered. The people who wrote the curriculum simply dodged the question of what to leave out.

When you overstuff a curriculum you guarantee that certain topics will be skimmed or skipped entirely and when you apply tremendous pressure on teachers to raise test scores, you force teachers to make the kind of choices you've seen here.

Antibiotics: an ever evolving story

I really think that the issue of antibiotic resistance gets too little play, so I am happy to see it discussed -- even if the discussion errs on the alarmist side.  In particular, I am unclear as to why we can't rotate antibiotics, why we even imagine that antibiotic soap is a good idea, and would be interested to hear a good reason for the routine use of antibiotics in raising cattle. 

The last is the strangest -- we are subsidizing meat production by not making farmers pay for the externality of antibiotic resistance.  I have no trouble with meat consumption, but it is unclear to me that it is an ideal target for subsidy given the high energy costs of that food source. 

However, it is true that we would still have options post-antibiotics.  Alcohol, heat treatments, and, surprisingly, silver remain effective despite antibiotic resistance.  Having said that, there is no reason we couldn't be doing more to make use of these techniques and rely less on the medications to which germs become resistant with time. 

Ed reform background reading -- three from Wikipedia

I know this is rich coming from a blogger but too many people are joining in on the ed reform debate without having taken the time to learn the basics (Frank Bruni being a veritable poster child), particularly when it comes to curriculum reform and Common Core. Below I picked three topics that are important and generally well known among people who have been in the weeds of the education debate but which seldom show up in the standard coverage. If you're interested in this debate, they're worth checking out.

The first is one of the biggest education reform initiatives to predate the current era. It had striking parallels to many of the current initiatives and was often supported by almost identical rhetoric but it seems to have dropped down the memory hole.


New Math

New Mathematics or New Math was a brief, dramatic change in the way mathematics was taught in American grade schools, and to a lesser extent in European countries, during the 1960s. The name is commonly given to a set of teaching practices introduced in the U.S. shortly after the Sputnik crisis in order to boost science education and mathematical skill in the population so that the perceived intellectual threat of Soviet engineers, reputedly highly skilled mathematicians, could be met.
...
Mathematicians describe interesting objects with set-builder notation. Under the stress of Russian engineering competition, American schools began to use textbooks based on set theory. For example, the process of solving an algebraic equation required a parallel account of axioms in use for equation transformation. To develop the concept of number, non-standard numeral systems were used in exercises. Binary numbers and duodecimals were new math to the students and their parents. Teachers returning from summer school could introduce students to transformation geometry. If the school had been teaching Cramer's rule for solving linear equations, then new math may include matrix multiplication to introduce linear algebra. In any case, teachers used the function concept as a thread common to the new materials.

Philosopher and mathematician W.V. Quine wrote that the "rarefied air" of Cantorian set theory was not to be associated with the New Math. According to Quine, the New Math involved merely..."the Boolean algebra of classes, hence really the simple logic of general terms."

It was stressed that these subjects should be introduced early. The idea behind this was that if the axiomatic foundations of mathematics were introduced to children, they could easily cope with the theorems of the mathematical system later.

Other topics introduced in the New Math include modular arithmetic, algebraic inequalities, matrices, symbolic logic, Boolean algebra, and abstract algebra. Most of these topics (except algebraic inequalities) have been greatly de-emphasized or eliminated in elementary school and high school since the 1960s.

The second is a widespread though perhaps fading approach to running a business. Outside of various questionable theories of incentives, it might be the most influential set of private sector ideas in the reform movement. (For a more detailed account of the relationship, check out this article by Shawn Gude)

Scientific Management

Its development began with Frederick Winslow Taylor in the 1880s and 1890s within the manufacturing industries. Its peak of influence came in the 1910s; by the 1920s, it was still influential but had begun an era of competition and syncretism with opposing or complementary ideas.

Although scientific management as a distinct theory or school of thought was obsolete by the 1930s, most of its themes are still important parts of industrial engineering and management today. These include analysis; synthesis; logic; rationality; empiricism; work ethic; efficiency and elimination of waste; standardization of best practices; disdain for tradition preserved merely for its own sake or to protect the social status of particular workers with particular skill sets; the transformation of craft production into mass production; and knowledge transfer between workers and from workers into tools, processes, and documentation. 

Scientific management's application was contingent on a high level of managerial control over employee work practices. This necessitated a higher ratio of managerial workers to laborers than previous management methods. The great difficulty in accurately differentiating any such intelligent, detail-oriented management from mere misguided micromanagement also caused interpersonal friction between workers and managers.

The third is rather specific and it's perhaps more up-and-coming than big, but it has some powerful supporters and is already having a having a major impact, particularly in mathematics education.

Deliberate practice

Psychologist K. Anders Ericsson, a professor of Psychology at Florida State University, has been a pioneer in researching deliberate practice and what it means. According to Ericsson:

"People believe that because expert performance is qualitatively different from normal performance the expert performer must be endowed with characteristics qualitatively different from those of normal adults." "We agree that expert performance is qualitatively different from normal performance and even that expert performers have characteristics and abilities that are qualitatively different from or at least outside the range of those of normal adults. However, we deny that these differences are immutable, that is, due to innate talent. Only a few exceptions, most notably height, are genetically prescribed. Instead, we argue that the differences between expert performers and normal adults reflect a life-long period of deliberate effort to improve performance in a specific domain."

One of Ericsson's core findings is that how expert one becomes at a skill has more to do with how one practices than with merely performing a skill a large number of times. An expert breaks down the skills that are required to be expert and focuses on improving those skill chunks during practice or day-to-day activities, often paired with immediate coaching feedback. Another important feature of deliberate practice lies in continually practising a skill at more challenging levels with the intention of mastering it.[4] Deliberate practice is also discussed in the books, "Talent is Overrated," by Geoff Colvin,[5] and "The Talent Code," by Daniel Coyle,[6] among others.

Points to Ponder

Ezra Klein:

In their ambition to simultaneously reformulate almost every major government program, Republicans have embraced an agenda of greater complexity and scope than anything Democrats now promote. An America in which the federal government can successfully run Medicaid but can’t build functional exchanges has no place for Ryan’s far-reaching reforms.

One of the advantages of simple and universal programs is that they are easy to administer.  When you have a country of 300 million people, it is not trivial to figure out who is entitled to benefits. 

Ironically, the sort of reforms where we match people more precisely to benefits are precisely the reforms that require really good government in order to work. 

Kennedy, Camelot and the danger of myth

"I just can't see a picture of Martin Luther King without thinking, you know, that man's terrible."
Jacqueline Kennedy, speaking in the months after her husband's assassination.

Over at the Monkey Cage, there's a political science take on the anniversary of the assassination (Why so many Americans believe Kennedy assassination conspiracy theories). It makes some interesting points but I have a somewhat different take.

As we've talked about before, if there's an idea that fits in with pre-existing beliefs (particularly one which alleviates cognitive dissonance) and which is aesthetically attractive, people will tend to favor that idea over better supported but less appealing alternatives.

The Sixties are a period that inspire intensely conflicting emotions, particularly among boomers, often producing great cognitive dissonance and there is probably no more resonant myth than that of a lost golden age (with loss due to betrayal being a particularly popular variant). In the case of John F. Kennedy, the Camelot allusions started almost immediately after the assassination and Johnson was soon identified with one of the most mythic of betrayers. (The use of conspiracy theories to delegitimize presidencies is, of course, not limited to LBJ.)

The power of these loss myths obviously rely on the counterfactual leading to a happy place. (if Orpheus and Eurydice were headed for a miserable marriage, the story isn't nearly as effective.) In the case of JFK, for many Democrats and boomers (particularly boomers who had been draft eligible), this basically means the great society without the escalation in Vietnam.

As for the latter, there is certainly evidence that Kennedy was seriously considering getting out, having come to suspect that the war was a lost cause, but every president from Ike through Nixon saw Vietnam as problematic, but every administration got us in deeper. Wars have a long history of being easier to get into than out of. Add to that JFK's commitment to fighting communism (particularly in Latin America and, because nothing ever changes, Iraq) and you can see how certain historians take this position:

Patricia Limerick, a University of Colorado history professor who heads the school's Center of the American West, doubts Kennedy would have backed off from U.S. involvement in Vietnam. The policy of communist containment was too ingrained in him.

"That was one Cold Warrior, that Kennedy," Limerick said. "He gave so much momentum to Vietnam. Cold War thinking was such a powerful arranger of brain cells of people of a certain age at that time."

The domino theory — the notion that communist expansion would continue unless directly confronted — drove decisions. Even the race to the moon was a direct competition with the Soviet Union.

"So I don't know any reason to think that foreign policy would have evolved," Limerick said. "Lyndon Johnson inherited a rat's nest, and we all know who he inherited it from."

How about domestic (and extraterrestrial) policy? Kennedy had laid out an ambitious "New Frontier" agenda but outside of research the progress had struck many observers at the time as somewhat slow, particularly on the social justice side. It's not entirely clear why that would have changed. Even when it came to Apollo, Johnson had been pushing the space race as early as the late Fifties and was, if anything, more dedicated to the issue than was Kennedy.

Of course, the cause where the difference is sharpest is civil rights. While Kennedy was certainly progressive on these issues, they were not a priority. Furthermore, there was considerable emotional distance between the Kennedys and the leaders of the civil rights movement, most notably Martin Luther King who was not even invited to JFK's funeral.

By comparison:

By this time in January 1965, Johnson had already driven through Congress the most important civil rights legislation since emancipation. Now, he told King, their work was only beginning. When Congress reconvened, he intended to introduce a voting rights bill, one that would bring justice to the segregated South, creating a vast new pool of loyal Democratic voters even as it would surely alienate multitudes of whites. ''The president and the civil rights leader -- the politician and the preacher -- were bouncing ideas off each other like two old allies in a campaign strategy huddle, excited about achieving their dreams for a more just society,'' Nick Kotz writes in his narrative history of the two men's alliance. ''As always,'' he continues, ''Johnson did most of the talking. As always, King was polite and deferential to the new president. But there was a shared sense of new possibilities, new opportunities for cooperation to bring about historic change.'' This carefully etched scene serves complementary purposes. It captures Johnson and King at the apex of their collaboration, a snapshot of an optimistic peak that only magnifies the friction and tragedy to come.

The standard response to the Kennedy-King antipathy has generally been to blame J. Edgar Hoover ("Caroline Kennedy, the daughter of John and Jacqueline, said her mother's comments about King are evidence of the 'poisonous' activities Hoover was engaged in, as he ruled the FBI as his private fiefdom."), but as appealing as this is from a psychological standpoint (the "bad council" excuse is often used to alleviate cognitive dissonance), there are at least a couple of problems with this explanation.

For starters, Hoover had constructed his empire in large part by being able to sense both what presidents needed to know and wanted to hear. Here's Tim Weiner, author of "Enemies: A History of the FBI."

GROSS: So did Hoover kind of make a lifelong practice of using his wiretapping to spy on people he perceived as his enemies in government?

WEINER: Well, that's correct, but he also was very well-attuned to what presidents wanted to hear. President Eisenhower wanted to hear about the communist threat. President Johnson wanted to know about the Ku Klux Klan, and despite his lifelong predilection for opposing integration, Hoover did as the president ordered. He was very sensitive to the needs of presidents.

More importantly, Johnson had heard the same FBI reports that Kennedy had but they had no apparent effect on his attitude toward King, though they may have shaped his feeling toward Hoover. ("It's probably better to have him inside the tent pissing out, than outside the tent pissing in.")

In other words, the golden age story here assumes that Kennedy was about to change direction on the two defining issues of the decade -- Vietnam and civil rights -- and that he was going to change in the right direction (right according to the belief system of those who tend to hold most tightly to the Camelot myth). This could well have happened during a second Kennedy term. Or we could have had withdrawal from Vietnam but no Head Start, Medicare, Medicaid, or Voting Rights Act. We might have even stayed in Vietnam and lost all of those programs.

Myths of golden ages and the loss of innocence are tremendously appealing in large part because they let us avoid facing the way things really are. With all due respect to JFK (who was, in many ways a great man), maybe it's time to let this one go.

Students will little note, nor long remember what was taught here...

[Update: For more on Common Core and David Coleman check out this follow-up post, "The great pedagogical end run"]

It was just over one hundred and fifty years ago that Abraham Lincoln delivered the Gettysburg Address. That makes this story from Valerie Strauss particularly timely:

Common Core’s odd approach to teaching Gettysburg Address

Imagine learning about the Gettysburg Address without a mention of the Civil War, the Battle of Gettysburg, or why President Abraham Lincoln had traveled to Pennsylvania to make the speech. That’s the way a Common Core State Standards “exemplar for instruction” — from a company founded by three main Core authors — says it should be taught to ninth and 10th graders.

The unit — “A Close Reading of Lincoln’s Gettysburg Address“ — is designed for students to do a “close reading” of the address “with text-dependent questions” — but without historical context. Teachers are given a detailed 29-page script of how to teach the unit, with the following explanation:

The idea here is to plunge students into an independent encounter with this short text. Refrain from giving background context or substantial instructional guidance at the outset. It may make sense to notify students that the short text is thought to be difficult and they are not expected to understand it fully on a first reading — that they can expect to struggle. Some students may be frustrated, but all students need practice in doing their best to stay with something they do not initially understand. This close reading approach forces students to rely exclusively on the text instead of privileging background knowledge, and levels the playing field for all students as they seek to comprehend Lincoln’s address.

The Gettysburg Address unit can be found on the Web site of Student Achievement Partners, a nonprofit organization founded by three people described as “lead authors of the Common Core State Standards.” They are David Coleman,  now president of the College Board who worked on the English Language Arts standards; Jason Zimba, who worked on the math standards; and Susan Pimental, who worked on the ELA standards. The organization’s Linked In biography also describes the three as the “lead writers of the Common Core State Standards.”

At the risk of deviating from the standards of close reading, this requires some context. The education reform movement, like all major movements, is an alliance between different groups with different agendas. One of the less recognized of these groups is well-intentioned educators who champion certain pedagogical theories that have proven to be hard sells. (David Coleman is, in many ways, the archetypal member of this group.) The reform movement's emphasis on standardization (note the 29-page script) has given them a chance to apply these theories on a massive scale without a lot of review and despite a lot of resistance.

This resistance is a major but largely unreported source of tension between movement reformers and teachers (particularly experienced and, ironically, effective teachers) who are reluctant to scrap proven approaches for ideas that can, frankly, sound a bit flaky. More on that later.

This post continues the Common Core thread that started here. It also relates to some of my earlier comments about rutabaga cults.

More Motley Foolishness -- Hydrogen is safe as a fuel, not as an investment

I spotted another doozy from Motley Fool. For a change, it doesn't involve Netflix or Disney, but other than that the formula is basically the same and the advice is, if anything, worse. As is often the case, the title gives you a good idea what to expect:

"Will This New Toyota Hydrogen Car Change the World?"

The story, by John Rosevear, is pretty much a retyped press release along with some standard pop science boilerplate on hydrogen fuel cells all delivered in MF's typical breathless style ("heavy bets on fuel cells — and hydrogen — as a way to power the automobiles of the future"). As always, MF is careful not to come out and say that this is the next big thing while being just as careful to downplay (or omit entirely) all the troubling facts that undercut their argument.

There's an old saying in military circles that goes "Amateurs talk strategy; Professionals talk logistics." When dealing with transportation technology, you might replace 'strategy' with 'features' and 'logistics' with 'infrastructure.' Transportation infrastructure often faces a nasty chicken/egg problem -- few people want to buy the vehicles until the infrastructure is in place and you can't get infrastructure funded until lots of people own the vehicles -- but with hydrogen fuel cell cars the problem is particularly acute. Not only is hydrogen somewhat difficult to handle, it is competing against a range of low and zero emission vehicles, all of which use well-established infrastructure. There is no county in America where you cannot get gasoline, diesel, natural gas, and electricity.

On top of that, you also have a serious concern about energy density. There simply is not that much power you can extract from a cubic foot of hydrogen, even under considerable pressure.Gasoline has excellent energy density. Diesel is even better. Batteries are constantly improving. With hydrogen, I don't see much room for improvement. Energy density isn't as much of a problem with stationary systems but if you have to carry your fuel around with you it's a big deal. The FCV has "two spun-carbon and aluminium tanks holding hydrogen gas pressurised to 700 bar (10,000psi)" for decent range. That's a solid piece of engineering by Toyota (which employs a lot of smart people) but you have to suspect that higher pressures will be very hard to come by.

I don't want to paint too grim a picture. It's possible that Toyota's FCV will lead to something major -- there could be an unexpected technological advance or a major government initiative that subsidizes both the cars and their infrastructure -- but based on current comparative functionality and infrastructure issues, this technology is very much a long shot.

More to the point, the challenges facing fuel cell vehicles are widely known and if you're reading something about investing in this sector, these challenges need to be prominently mentioned very near the top of the page. If they aren't, you need to ask yourself how much value to put on the writer's advice.

Pre-existing conditions

Mark Palko sent me a link to a Consumer Reports discussion of pre-ACA individual market healthcare.  It was scathing, giving examples like:

The Georgia real estate agent whose group health plan was folding and who couldn’t find replacement insurance unless it excluded coverage of her $1,700-a-month rheumatoid arthritis medication, without which she would quickly become disabled.

I think that the example above gives a good example of what makes the market in health insurance challenging.  When you link your insurance to your job, some people will inevitably lose their jobs.  These people will have paid into insurance when they were healthy but no longer have access to that plan.  Thus they have serious problems ever getting coverage.

Now this would be fine if acute risks were all that we were insuring against (like a house fire).  But we also insure against the development of a chronic condition that is expensive to treat and ongoing.  Now add in recission -- health plans checking to see if you gave perfectly accurate information only after you start claiming benefits (notice that they do not offer to return previously paid premiums as part of this process) and it is clear that the individual health plan market had some serious drawbacks.  In fact, given recission, it is unclear if people who lose inexpensive plans were actually insured in the case of a disaster. 

Now the private market solution to this set of problems is a regulated series of exchanges.  If these exchanges cannot be made to work, and even private companies seem to have trouble with doing so from time to time, the next best solution would be to expand public coverage.  What if anybody could opt-in to Medicaid?  Would that really be a disaster?  It would hurt medical wages and simultaneously expand demand, but we could compensate by expanding medical licensing to groups like Nurse Practitioners provide care to Medicaid patients.  Then private insurance is supplemental (like the UK) and these issues become a lot less concerning (because insurance reputation begins to really matter). 

These issues are worth keeping in mind as we watch this experiment unfold.   

2... 4... 6... 8... Time to disaggregate -- Motley Fool/Netflix Edition

[second in a thread]

Another example of why I'm uncomfortable with the quality Motley Fool's analyses, this time demonstrating a crude but common statistical misstep (or in some cases, distortion). The analyst here is MF regular Tim Beyers (not familiar enough with MF to say why it's in the third person).

Netflix offers each new Marvel show international distribution to as many as 40 million viewers worldwide. Disney can't achieve that on its own, Tim says, because it controls a limited number of channels for offering live action superhero content and ABC already airs Marvel's Agents of S.H.I.E.L.D.

History also favors the deal. More than 66% of gross receipts for Iron Man 3 came from overseas territories. Thor: The Dark World is also tracking well in foreign territories, much like its predecessor. Settling for U.S.-centric distribution would be aiming too low, Tim says.

If you've been following the Netflix story in any detail, one component of this argument will jump out immediately but anyone who works with data will probably have at least a hunch about where this is going.

The phrase "40 million viewers worldwide" raises the question, how many of those viewers are overseas? The answer is less than ten million. For comparison, here's how HBO breaks down:

As of September 2012, HBO's programming reaches approximately 30 million pay television subscribers in the United States, making it the second largest premium channel in the United States (Encore's programming reaches 35.1 million pay subscribers as of March 2013). In addition to its U.S. subscriber base, HBO also broadcasts in at least 151 countries covering approximately 114 million subscribers worldwide.

What's worse, those overseas Netflix viewers seem to be mostly in Europe, with little apparent presence in the all-important Asian market.

Perhaps there's more going on than we know about. Netflix could be on the verge of a big international expansion. For now though, Netflix is not a major international power compared to companies like Time Warner and while the new Netflix/Disney deal may turn out great for both parties, arguing that it's a good idea because you wouldn't want to be too U.S.-centric probably tells us less about the stock and more about the quality of the analysis.

More (Reluctantly Reported) Motley Foolishness

I was going to let the Motley Fool thread drop. They kept coming out with analyses and advice that I was tempted to comment on but I was afraid the comments would start to sound the same.

Recently, though, I saw a headline I couldn't resist clicking on. As a result, I found a whole new reason to worry about people basing investment decisions on MF recommendations. [still more have showed up since I wrote this. I'm afraid we have another thread coming.]

Just to review, when ABC announced  S.H.I.E.L.D., expectations were high. The Avengers had been one of the most successful movies ever and, based on the box office of the first semi-sequel, Iron Man 3, interest was showing no sign of fading. Nowhere were these expectations higher than at Motley Fool which came out with a list of reasons why  S.H.I.E.L.D might actually turn out to be bigger for Disney than the Avengers had been.

I pointed out at the time that this would have required a huge, historic hit and that none of the reasons listed in the MF post came close to supporting the claim.

Time passed and ratings rolled in.  S.H.I.E.L.D had very respectable ratings, but they fell somewhat short of expectations. More worrisome has been the trend: ratings have been slowly but steadily dropping since the debut.

Now Steve Symington, the MF contributor who provided the previously mentioned post, has posted a response to the news and it unintentionally captures a lot of what bothers me about Motley Fool, starting with the title:

"Skeptics keep panning Marvel's 'Agents of S.H.I.E.L.D.' for its seemingly lackluster overall ratings, but here are several reasons Disney couldn't be happier."

First of all, to get the obvious out of the way, Disney could and would be a lot happier with better numbers. For this show to live up to anywhere near its potential as a tentpole, It would half to be both a bigger and a demographically broader hit and it would need to generate lots of real time view.  There is no real tentpole effect for viewers watching on Hulu and delayed viewing greatly undercuts social media buzz on places like Twitter which thrives on the shared experience of simultaneous viewing.

None of this is disastrous. The numbers for the show are certainly not bad. On top of that, keeping the show around helps strengthen the relationship with Joss Whedon who has proven to be a very valuable asset to the franchise. Still, there's no way to get around the fact that, while there are bright spots, there is no major area where the show is exceeding expectations and there are a number of areas where it is falling significantly short.

Put another way, one of Disney's assets turned out to be worth less than was anticipated. There are various ways for investment councilors to handle situations where predictions prove directionally wrong. They can reassess their advice. They can argue that the adjustment is fairly small relative to the size of the company (difficult once you're on record as saying the asset could be bigger than the Avengers, but certainly valid in this case). What you never want to see is a councilor looking for reasons to justify previous positions. This is a natural response to cognitive dissonance but it's deadly for stock pickers.

The MF piece is filled with attempts at self-reassurance. Bright spots are trotted out without addressing the possibility that the market had already priced in anticipated numbers that were as good and usually better than what we've seen. Desperately upbeat language is used ("incredible staying power," "run up the score") while a negative but accurate statement like "continue to fall" prompts scare quotes.

Perhaps the most telling though, is what's not in the post. If you take a look at this post from TV by the Numbers after reading the Motley Fool piece, you'll notice a couple of interesting points. The arguments and wording are remarkably similar but one phrase that appears in the second post is nowhere to be found in the MF article:

"via press release:"

Weekend blogging -- a few more for my to-see list (Truffaut edition)

As mentioned before, I have a long list of films of films that I should have gotten around to in college. One of these days, I should just go ahead and sign up for Hulu Plus see I can get access to the entire Criterion Collection (probably after I finish up with Netflix). On the other hand, I might actually end up seeing more if I continue catching the free-for-the-__- days selections (that time limit is an excellent motivator)

This week the freebies include a dozen by François Truffaut.

Weekend blogging -- channeling my inner Sherlock nerd

As mentioned before, I'm a big fan of the show Sherlock, for my money the best of the myriad adaptations of the character. That said, I hadn't gone back and rewatched any of the episodes until I went online to find out when we could expect the season and came across this.

The second series concluded with "The Reichenbach Fall". Steve Thompson wrote the episode, which was directed by Toby Haynes, who had previously directed many of Moffat's Doctor Who episodes. First broadcast on 15 January 2012, the episode follows Moriarty's plot to discredit and kill Sherlock Holmes, concluding with Holmes faking his suicide as Watson looked on. It was based upon Conan Doyle's story "The Final Problem", in which Sherlock and Moriarty are presumed to have fallen to their deaths from the Reichenbach Falls in Switzerland. Moffat felt that he and co-creator Gatiss had outdone Conan Doyle in their version of Holmes' fall and Moffat added that, in that much-discussed sequence, there was still "a clue everybody's missed"

The Wikipedia article lead me to this quote from Moffat: "It's not a cheat. We've worked it out. It all makes sense."

I decided to go back and check out the rooftop sequence. I'm pretty sure I spotted the clue he was talking about (hint: it occurs very early in the scene) and I believe I've got the rest of the clues as well. I'm putting them after the break. If you feel like playing along, scroll down but be warned, it's all spoilers and nerdiness from there on.

I always feel a bit guilty, or at least apologetic, about this kind of post. God knows I've made fun of plenty of fanboys in my time. I will, however, offer a couple of defenses for this one case: first, Moffat really is inviting us to go for it; and second, one of the most appealing traits of this generation of British TV writers is the care they take not to abuse our suspension of disbelief. Once we've accepted the premise, they will make sure that everything that follows, no matter how surprising, will be believable in terms of plot and consistent in terms of character.

The first time I watch a Moffat and friends show, I simply go along with the effective drama and comedy. Later, I'll peek behind the curtain and look at the machinery, but when the story's good enough, that just adds to the fun

Common Core and the Law of Large Numbers

Common Core is a big story that needs to be addressed in depth (Valerie Strauss's column is a good place to start), but a lot of the devils are in the details and one of thee peskiest of those devils (call him the Mephistopheles of education reform) is what happens to high-sounding ideas on the way to actual classrooms.

Let's take the proposed standard that all students should understand the law of large numbers. This a wonderful goal, but before we add it to the curriculum, we need to think about the Luskin effect. Donald Luskin is the CIO for the consulting firm Trend Macrolytics. He's also a widely read columnist and commentator on financial matters. He's someone who ought to understand sampling and who thinks he understands it, but he really, really doesn't.

You will occasionally find an algebra teacher who obviously doesn't understand something like factoring trinomials, but that's rare. Finding a high school algebra teacher (or for that matter, a university math professor) who doesn't understand probability theory is not that uncommon and a sufficiently clueless explanation can be worse than letting the topic wait until college.

When I Googled common core "law of large numbers" this was the first non-video that came up:.

By (date), when given (5) problems involving interpreting results from a simulation using The Law of Large Numbers (i.e. (# of times an event happens) / (total # of trials) approaches the theoretical probability for the event as the # of trials grows large), (name) will correctly solve (4 out of 5) problems.

Example: A student rolls a fair, 6-sided die 10 times and gets the following results: 4, 2, 4, 3, 5, 6, 6, 2, 4, 6. How many times do you expect that the student will roll a 1 after 600 rolls?

Answer: P(rolling a 1) = 1/6, (1/6)*600 = 100 times

This is a terrible example though there's some ambiguity about exactly why it's so bad. If they mean 'expected' as in 'expected value' then the answer is technically correct but has nothing to do with the law of large numbers. If they mean 'expected' in the common usage sense, the answer is just wrong.

I checked few of the other links from my Google search. Lots had simulation results (which was a good first step) but I don't think I saw any that truly got the concept, at least not well enough to explain it. Better than this but not that much better.

Concepts like the law of large numbers are not deadwood -- they are important and useful and if you can actually find a way for students to master them you should do it -- but they share a common problem with jetsam like synthetic division. There is always an impetus to add them to a curriculum but little counterbalancing pressure not to waste students' time.

The announcement of a new curriculum is invariably followed by a round of hearty round of self congratulations and talk of "keeping standards high" as if adding a slide to a PowerPoint automatically made students better informed. It doesn't work that way. Adding a topic to the list simply means that students will be exposed to it, not that they will understand or master or retain it.

If we start talking about setting aside significant time to cover probability and statistics accurately and in reasonable depth and put the ideas in proper context, you have my enthusiastic support, but until then maybe we should focus on the understanding, mastery, retention of the stuff that's already in the curriculum.

Yikes

There is a pension show-down as part of the local contract negotiations at Boeing.

Take one aspect of the Boeing showdown, the pensions. For decades Boeing has given its line workers a decent retirement benefit. It pays out about $90 a month for every year worked at the company, so that someone with 30 years of service would get $2,700 a month when they’re done at age 65.

Add Social Security to that and you’ve cobbled together a comfortable but hardly posh old age for sheet-metal workers, riveters and others who build the nation’s planes.

Boeing wants to cancel those pensions and put in much weaker 401(k) plans. There’s little doubt this will happen, sooner or later. Because if it doesn’t, Boeing can use pension-free laborers in South Carolina to do the same work.

It’s a race to the bottom. Or rather, a slog to an era when workers will be more reliant on Social Security than ever.

So what’s most galling is that Boeing’s CEO is out pushing to cut back on the nation’s retirement plan as well.

In recent years Boeing CEO Jim McNerney has headed the Business Roundtable, a lobbying group of top U.S. corporations. Earlier this year that group called for raising the eligibility age for Social Security to 70 years old, as well as crimping back on the benefits (by reducing the index of inflation used to calculate payouts.)

“We are going to need our employees to work longer just to fill the needs that we have in the work force,” said a Roundtable suit, helpfully explaining why all Americans should willingly retire later, for less.

I don't necessarily want to comment on the merits; Megan McArdle does a good job of presenting the pro-contract side and it was pretty well thought out.  So what I find odd in this constellation of issues is that traditional approaches to recruiting workers are being dismissed.  The CEO of a major companies is puzzled about how to incent workers not to retire at 65.  In my strange quadrant of the gamma sector, we have this thing called "wages" which are often linked to "benefits".  It's a strange paradox, but consenting adults gladly take on employment in exchange for the good and services that they can acquire with these "wages".   

Now it is true that wages have to be higher when the decision isn't "work or starve".  But that is probably a feature and not a bug -- we would like older adults who are less capable to have the option to retire.  There are many options for expanding the workforce.  Immigration for example, started now, would have wonderful effects in about twenty years.  There are a lot of young people who arrived as children and have grown up in the United States who might be willing to help bolster the labor reserve, if there really is this kind of epic crisis underway. 

h/t: Eric Loomis (who I initially thought might be making this up)

Just a quick dip of the toe in the water

One of the interesting pieces that is coming out about some of the high performance charter schools suggests that at least some of their success is due to selecting the most promising students.  These posts, from New Jersey and Arizona, is due to selecting students from higher income families (less school lunch eligible kids), less learning disabilities, and expelling problem students.  Clearly any school that engaged in these tactics would do better relative to public schools (who have a mandate to accept these students and an accountable procedure for expulsions). 

I am reminded of parents I know who had their kids "kicked out" of daycare.  The theory was a private daycare can select who will and will not be in their clientele and remove kids who do not "fit in".  And good for them -- that flexibility is a key part of private business and it can be useful to be able to focus on people your model is compatible with. 

But we should realize that this business model flies in the face of the ideas of universal schooling.  I challenge you to look at the chart on African-American male students in Northstar and not worry.  It's nearly a complete attrition over the course of the cohort's lifespan.  It seems incompatible with any strict definition of a 100% graduation rate, unless all of these children went on to transfer to and graduate from public schools.  If we value universal education as a public good and an underpinning of American prosperity then maybe we need an approach that is actually designed to do this? 

I will also note that it is a key principle of outcomes analysis that you need to look at what happens to the study drop-outs when evaluating an intervention.  After all, all of the adverse events on a drug could happen in the post-drug quitting phase.  This is not evidence of safety.  Nor is sending children who are struggling to public schools evidence that you are able to meet these children's educational needs. 

I would be shocked if Mark Palko didn't have a much more detailed analysis to follow this up. 

Distracted Driving

A classic case of a serious externality:

According to a new study published in Public Health Reports, the rate of distracted driving-related fatalities per 10 billion vehicle miles traveled went up from 116.1 in 2005 to 168.6 in 2010 for pedestrians and from 18.7 in 2005 to 24.6 in 2010 among bicyclists. However, distracted driving-related deaths among motorists decreased over the same time period — a trend that study authors said mirrored overall motor vehicle fatalities and may be attributed to safer vehicles. Unfortunately, cyclists and pedestrians don’t have such protection on the road. In fact, distracted drivers were 1.6 times as likely as nondistracted drivers to mortally hit a pedestrian at marked crosswalks and about three times as likely to hit a pedestrian while on a road shoulder.

Much as I am terrified by the movements of pedestrians, I do think that this statistic makes it clear that distracted driving leads problems.  Even hands free devices have had mixed success with making drivers safer while talking.

It seems a classic case where regulation would be useful.  Maybe cell phones should stop working in a moving vehicle? 

What do these two things have in common?

Standard and Poor's defense against misleading ratings:

S&P said in its request to dismiss the case that the government can’t base its fraud claims on S&P’s assertions that its ratings were independent, objective and free of conflicts of interest because U.S. courts have found that such vague and generalized statements are the kind of “puffery” that a reasonable investor wouldn’t rely on.

So lying about the results of your financial analysis (for profit) and misleading people who rely on information is okay?  Do these people not know that accurate information is an absolute requirement for markets to work and that ends up being a classic principal agent problem? 

And then consider this case:

It was also the beginning of the end.  The Journal at first identified her as just an analyst for the Institute for the Study of War. In other op-eds, O‘Bagy herself had disclosed the dual association, but for the Journal, at the insistence of Kim Kagan, the Institute’s head, she says, she did not. Kagan disputes this account. Critics were quick to point out the Journal’s omission of O’Bagy’s task force work, charging that she was lobbying the same politicians she was meant to be briefing. O’Bagy and the task force both say she was never involved in the group’s lobbying activities. But that first opening led others to look more closely. Within days, it was revealed that Dr. O’Bagy didn’t have a PhD.

I think that these are both parts of the objectivist ideals that have penetrated American society.  It has replaced ideas like "it's not whether you win or lose but how you play the game" with an ideal of winning as being a sign of moral worth. 

Objectivism definitely has a "do what you want element".  Consider:

Why do they always teach us that it's easy and evil to do what we want and that we need discipline to restrain ourselves? It's the hardest thing in the world--to do what we want. And it takes the greatest kind of courage. I mean, what we really want.

It is not that there is no value in this approach, but one can easily imagine how this can lead to people running roughshod over others in the climb up the slippery pole of success.  I think that this is worth giving a lot of consideration to. 

What is the role of truth, self-discipline, and good conduct in the modern world? 

Weekend blogging -- checking a couple off the list

If there's a film lover's equivalent to David Lodge's literary parlor game humiliation (where you list the most famous/important books you haven't read), I'd be one hell of a competitor. This weekend, though, I plan to knock off a couple of longstanding items from my to-see list.



If you want to catch this first one, hurry. Free viewing expires in a couple of days.




I also need to see Diabolique as background for a post I plan to do one of these days on the odd critical rise of Vertigo, but more on that later.

There is a long history of this type of bad judgement in literature

It dates back to Ivanhoe, who clearly picked the wrong girl -- the less interesting and compatible partner.  It looks like the Marvel version of Thor has the same problem.  Curiously, the mythical Thor actually picked Sif so maybe he will change his mind eventually?

Twitter's 140 -- the fast and the freshest

In response to my previous piece about Twitter, Joseph suggested that the 140 character limit forces writers to terse. I'm not so sure. I think the more common response has been a tendency toward annoying abbreviations, elliptical writing, and small subjects.

This did, however, get me thinking about the possibility of other reasons for the character limit, and I was forced to admit there are a few.

For starters, there's speed. The short length encourages writers to wrap up their thoughts and get them out the door. I am sure there are those out there who labor over each tweet as if composing a haiku, but for most of us very little time elapses between when a thought hits and when the tweet button is hit.

That speed leads to a number of other traits which are desirable for the platform. It more or less guarantees a healthy flow of traffic. You can find a rapidly flowing stream of tweets on almost any subject imaginable.

Compared with blogs, the brevity of tweets can make exchanges feel more like conversations than debates. This gives Twitter a distinct and inviting feel.

Perhaps most importantly, that speed also allows Twitter to be the most up-to-date of news media. When it comes to getting detailed, real time information during a big, complicated crisis, Twitter is exceptionally good, in large part because the users are constrained to produce short, fast bursts of information.

I still think that the Harrison Bergeron effect – setting up an artificially equal playing field for mobile and nonmobile users – is the most important aspect in the success of Twitter, But there's certainly more to the story.

Driving versus walking

We are late to this party but consider:

When it comes to energy use and greenhouse gases emitted, appearances can be grossly deceiving. Granted, people who drive everywhere are energy users and polluters. But walkers also use fossil fuels through the food they eat to replace the calories burned while walking. Of course, driving can be more polluting under some circumstances, such as when large SUVs are the preferred vehicles or when drivers insist on doing wheelies at every stoplight. Bicycling the distance can also be less polluting than driving. Dunn-Rankin sums up the central, largely counterintuitive, point of this commentary: "Driving a small [or moderate-size] car and not having to replace burned calories saves more energy (and greenhouse gases) than walking when the extra calories expended are replaced."

Tim Stuhldreher jumps on the biggest issues:

First, if you’re going to look at the entire food chain to determine the energy cost of human walking, it’s only fair to do the same thing for the car. That means you have to factor in the energy costs of producing it. It’s not clear how much that adds, but it’s significant: Estimates range from 10 percent to 100 percent and everywhere in between. I’m not going to speculate on the exact number, but if it’s 50 percent to 100 percent, then we’ve just put walking right back on par with driving, mile for mile.
 

Second, Dunn-Rankin’s result depends on the use of a high-mpg car, around 40 miles per gallon. If you drive a pickup truck or an SUV, your mileage is worse, and you have to adjust the figures accordingly.

 Third, doing this calculation on a per-mile basis ignores the obvious and important point that people typically drive much farther than they walk. No one buys a car to go half a mile here, a quarter-mile there. Moreover, land use patterns change as cars become more prevalent in society – you get less density and more suburban sprawl. To see the real impact of driving vs. walking, you have to take that into account.

I think the last point is the most salient.  The argument also has other issues -- like if we used bicycles instead of cars for the commute then the bikes would be a lot safer and people would be a lot more physically fit.  It may be implausible to walk twenty miles to work but I have met people who actually do it by bike.  Heck, it is also possible that people would lose weight, become more efficient as a result, and actually generate less emissions themselves. 

Furthermore, this assumes that the same fossil fuel use would remain in agriculture while being removed from personal use.  And that more efficient ways of agricultural transport could not be found (or that we couldn't alter our diet by season).  

It's a point mostly of interest to see how far people will accept the counter-intuitive as true, just because it is so at odds with conventional wisdom.  Sometimes the conventional wisdom exists for a reason. 

Service Contracts

From the local Mad Biologist:

Yes, there are people who will give away their information at the drop of a hat for a ten percent-off coupon. But many of us have no choice in the matter. When you sign the terms of agreement for an internet provider, credit card company, or many other businesses, you are offered a take-it-or-leave-it contract. No negotiation is possible. And these contracts are often for nearly-essential services. Sure, you don’t need a credit card, an internet connection, or an email account, but it’s hard to function in 21st century America without these things.

These are often de facto monopolies (e.g., cable companies), or else you are offered a very limited number of options that really don’t differ that much (e.g., wireless providers). In a common law sense (and the last thirty years of neoliberal and conservative jurisprudence have essentially annihilated the notion of common law), a contract that you can’t negotiate for a service you basically can’t do without isn’t really a contract, it’s extortion. Worse, this unequal (one might use the word servile) relationship is often sanctioned by the government.

 This is a bit strident, but basically correct.  Boilerplate contract that cannot be easily negotiated in individual cases is a nice legal defense but rather misses the point of agreements.  The imbalance in market power is really the problem and the services have become increasingly essential.  Try not having a credit card, a bank account, telephone, or internet access.  People due survive in these circumstances, but the level of cost to avoiding these contracts is high. 

Now when the contract is reasonable that is one thing.  But isn't the idea of a universal reasonable standard of interaction seen elsewhere?  Or was I dreaming during the "government regulations" phase of my education? 

Free TV blogging -- subtle signs of a tipping point

It may not look it, but I think this might be kind of a big deal.

As (very patient) regular readers know, I've been following the over-the-air television story for a long time, partly because I'm a satisfied user but mainly because there's a push to shut down the medium and I believe that the loss of OTA television would reduce media diversity and acerbate the effects of income inequality.

There's been a definite progression in coverage since the conversion to digital in 2008. Other than a few pieces specifically on the conversion (such as this very good story from the LA Times and this not-so-good one from the NYT), there was almost no mention of the new medium for the first year or so.

Then came the comment stage: articles about relevant subjects like cable problems and cord-cutting would make no mention of OTA options but the comment sections were full of readers saying "what about rabbit ears?"

The CBS/Time Warner dispute prompted another stage marked by a considerable increase in coverage. With the largest markets in the country losing cable access to the number one network, reporters more or less had to discuss other options for viewing television. The resulting stories were of somewhat uneven quality, but they did start addressing over-the-air as a viable option.

Now we have what might turn out to be the fourth stage in the coverage. Here's a passage from a recent post by Brad Reed of the tech site BGR complaining about Comcast's service:

Now, I know there are solutions to this. I plan on installing a digital antenna and unplugging the Comcast cable all together so I can once again watch football in HD. But it’s appalling to me that Comcast has sent me a product that the company has billed as an “upgrade” that has actually downgraded the quality of my service dramatically. What’s more, Comcast is telling me I’ll need to pay an extra $10 a month to access channels that are free to access over the air.

The worst part about all this is that I’ll have little choice but to continue paying Comcast for a television service that I’ll never use simply because the company’s glorious bundling plans make it cheaper for me to have TV and Internet than just Internet alone. And it’s not like I can switch providers since Comcast has a regional monopoly in my area.

I do have one small quibble with this story – there is no such thing as a digital television antenna – but on the whole this is the kind of story we've been waiting for: A writer for a tech savvy site who knows what is available over the air and who understands the value of having an option to a cable monopoly. This was almost impossible to find a couple of years ago.

One of the points I've been hoping/meaning to get across (as a blogger, I've always had a poor conception-to-expression ratio) is that competition is only meaningful if customers know their options.   That knowledge is not automatic. It has to be derived from personal experience, word-of-mouth, journalism/media coverage or marketing.

When you have a new product (and digital OTA is a new product, as or more distinct from analog OTA than cable was from that same medium thirty-five years ago), customers are particularly dependent on coverage and marketing to tell them they have another option. Unfortunately, most companies with major marketing budgets had a vested interest in the failure of the free TV model while the media had no interest in the story for a number of reasons, starting with the fact that companies like Weigel Broadcasting didn't have top dollar PR firms writing the journalists' stories for them.

As a result, there was a real danger that the new medium was going to be chopped up and sold for parts before the slow dissemination of information through direct experience and word of mouth could reach critical mass. For a time, I thought it was the likely outcome. Now, I think the odds for OTA are looking pretty good. The technology has always been more than competitive. Now that journalists and tech writers are including antennas in their discussions of television, that technological edge can start making a difference.