'Confidence' and 'Rationality'

This post by Andrew Gelman suggests replacing "confidence interval" with "uncertainty interval" based in part on the "awkwardness of explaining that confidence intervals are big in noisy situations where you have less confidence, and confidence intervals are small when you have more confidence."

At the risk of putting words into Dr. Gelman's mouth, his concern is partly about the confusion that often comes from assigning common words specific technical meanings that are subtly different than their common usage. 'Confidence' here doesn't quite mean what people think it means.

One way of addressing that concern is finding new terms that don't have the same potential for confusion. Another is finding better ways of explaining the distinction. But the very fact that this is a concern illustrates an important difference between statisticians and economists.

Both statisticians and economists take common words and assign them specialized meanings. Of course, this is a reasonable, even necessary, process. As thinking in a field becomes more precise, language has to follow suit, which is why you can find a similar process in many other disciplines, but the difference in attitudes toward refined words seems particularly marked in these two.

Based on anecdotal but extensive evidence, statisticians (and I'm definitely guilty of this) constantly, almost compulsively, stop to point out that what we said isn't what you think we said. This is especially true for 'significance,' which often comes with a brief (and unwelcome) lecture on p-value and types of error. This is part of the culture of statistics. We are taught early and repeatedly that the distinctions we are making are important and need to be spelled out explicitly.

Compare this to the way economists (particularly a freshwater economists) tend to use terms like 'rational.' When economists say an actor is rational, they mean that this actor's behavior can be modeled using a simple but highly restrictive set of assumptions. Many behaviors that qualify as rational in the common sense of the term fail to meet these assumptions while more than a few behaviors that do qualify would strike most people as irrational.

But unlike statisticians, economists generally don't feel compelled to spell out these distinctions. You will often see economists using phrases like "Are people rational?" These phrases are occasionally followed by 'in the economics sense,' but they are seldom accompanied by an explanation of just how narrow this sense is.

When an economist says "people are rational" or (Steven Levitt's preferred variation) "people respond to incentives," most listeners tend to take away the impression that they mean "people act in ways that are generally considered rational" or "incentives can change the way people behave." These latter statements are completely reasonable. Most of us would agree with them. They are not, however, what the economist meant.

Wall Street Bonuses and Motivation

Felix Salmon links to a Washington Post article about large “wall street” bonuses:

Fortunately, there were many happy students - and the happiest were by no means the best paid. The most important factor behind job satisfaction was how supervisors handled performance appraisals. Bosses who took the time to give real feedback had happy employees. Those who blew it off had resentful and confused workers.

"Given that junior employees were spending 90 hours per week at work," one student wrote, "we all wanted to be recognized for our efforts."

For many executives, the myth that a big bonus is enough to ensure motivated employees persists. But at least for this next generation of business leaders, it's simply not true. When the public is already infuriated by outsize bonuses for chief executives, clinging to this model is a bad idea. Management matters. Good management pays off. Bad management - including ignoring management altogether - will cost us.

I think that this is an insightful point. It can be taken too far (high levels of compensation do make up for a lot of frustrating moments) but I think that the idea of "fairness" and "predictability" are key items. It's worth a lot to know that you will make $80K this year. Replacing that with a 50% chance of $40K and a 50% chance of $200K is not the same (even if the expected value is higher). Now, if you remove robust feedback and clear expectations than it is only reasonable that workers will not feel like they can predict what the outcome of their year end review. That will be highly demoralizing (and take even higher levels of compensation to correct for).

This principle actually goes back to Adam Smith (if not before). He (paraphrasing the original passage) pointed out that, for a worker paid by the piece, that you not only have to compensate the worker for all of the time spent between jobs but also for the anxiety that the worker suffers.

Is it really efficient to import this type of model to areas like education?

NIH Merger

From DrugMonkey:

Instead it makes it look very much as if NIAAA is being subsumed into NIDA simply to make statutory way for the creation of this new translational medicine Center.

And that is a whoooole ‘nother ballgame. Because the discussion now should be “Is NIAAA worth losing in favor of the new Center?”.

To remind my readers, my approval of the NIDA/NIAAA merger is based on the stipulation that merging ICs is a good idea, will lead to efficiencies, etc. And that there is a general will to further scale back the number of ICs. Given this motivation the NIDA/NIAAA merger is about as obvious as can be. If those goals are not a given, then I’m in a very different stance about this current merger.

And I really, really do not like disingenuous bait-and-switch arguments. This is starting to smell like one.

I was never really sold on the merger, myself, as I thought alcohol research was different (in some interesting ways) then research on other recreational drugs. That being said, I wonder if (at some point) it might be worth rethinking the 27 centers from first principles and making sure that they are the one that best serve the goals of public health?

Testing the Jump$tart Test

The Jump$tart Coalition is a leader among organizations seeking to improve the personal financial literacy of students from kindergarten to the university level. In particular, through its biennial survey of high school seniors—the results of which you will hear about shortly—Jump$tart has brought increased attention to the need for greater financial literacy among the youth of our nation. During the Jump$tart survey’s 12-year history, the data gathered have served as the basis for useful measures of what young adults do and don’t understand about finances. Undoubtedly, we will soon learn that there is plenty of work to be done and that our students have much to learn.

Ben S. Bernanke at the Jump$tart Coalition for Personal Financial Literacy and Federal Reserve Board joint news conference, April 9, 2008

April of 2008 was definitely a time of signs and portents. Many economists and a few farsighted journalist like the good people at This American Life were warning us that we were entering dangerous territory. It's fair to assume that Bernanke didn't need the warning -- the man had essentially spent his entire career preparing for this crisis -- but he took time out of what was unquestionably a very busy day to laud the accomplishments of the Jump$tart Coalition and its survey.

It's easy to understand why Chairman Bernanke was concerned about financial literacy. With the complex, unstable economy, the shift away from traditional pensions and the constant flood of new financial products, financial literacy might be more important now than it has been for decades. You could even make the case for financial illiteracy being a major cause of the economic crisis.

But if the supporters of financial literacy need a good measure of how well we're doing, they'll need to find a better instrument than the Jump$tart survey.

The 'test' part of the survey consists of thirty-one questions. That's not very long but that many questions should be sufficient for a tightly focused, well-structured test. Unfortunately the focus of the Jump$tart survey is ridiculously broad, ranging from investments to retirement to credit cards to debt counseling to auto insurance to macroeconomics to really questionable career advice.

Even within the categories the questions have a random, pulled-from-a-hat quality with no apparent effort to prioritize. There are multiple references to credit histories but no mention of credit scores. None of the few questions on credit cards mention teasers or other cases where rates can change on a credit card. There are no questions that refer to charts or tables though the ability to read both is an essential part of financial literacy.

On the individual question level the situation is no better. Most of the questions are either badly written, trivial/irrelevant, open to interpretation, guessable or factually challenged. The test resembles nothing so much as the homework paper a student teacher might turn in when asked to come up with 31 questions on financial literacy.

If you compare this test to something like the SAT where every question has been repeatedly proofed, tested and rewritten, it becomes obvious how sloppy the writing is here, complete with rookie errors like using the wrong person in a question like this:

24. If you went to college and earned a four-year degree, how much more money could you expect to earn than if you only had a high school diploma?
21.9 a.) About 10 times as much.
8.6 b.) No more; I would make about the same either way.
22.0 c.) A little more; about 20% more.
47.6 d.) A lot more; about 70% more. *

[note: Numbers to the Left of Answers are Proportion Giving Response. The asterisk indicates the correct answer.]

What's the problem with using the second person here? This is one of those statements that's true for a population at large but may not be true for most subgroups of the population. The value of a college degree varies greatly based on proposed career plans. For an architect or database analyst, a ten fold increase would probably be conservative; for a truck driver or someone who plans to work in a family restaurant, a college degree may provide nothing but personal growth opportunities and bragging rights.

Another rookie mistake is the high number of guessable questions, questions where students who know nothing about the information of interest have a good chance of guessing the right answer.

18. Don and Bill work together in the finance department of the same company and earn the same pay. Bill spends his free time taking work-related classes to improve his computer skills; while Don spends his free time socializing with friends and working out at a fitness center. After five years, what is likely to be true?
11.5 a.) Don will make more because he is more social.
9.8 b.) Don will make more because Bill is likely to be laid off.
67.9 c.) Bill will make more money because he is more valuable to his company.*
10.8 d.) Don and Bill will continue to make the same money.

By the time they reach high school, students have long since learned the simplistic moral vision of tests and textbooks. When in doubt, pick the answer that shows hard work and self-discipline pay off. Questions like this may be better measures of students' cynicism than of their financial literacy, particularly given the suspect answer.

As Frances Woolley observes, it is "not at all obvious to me that (c) is the right answer." In most companies, the management track tends to pay better and move faster than the technical track, making (a) a reasonable choice and, in a age of off-shoring, the employee who just brings computer skills to the job is particularly vulnerable to replacement, making (b) a possible choice. In other words, you could argue that the 'correct' choice is neither the best nor the second best answer.

In order to provide useful data with tests and surveys, you have to make sure that the response to each question tells you what it's supposed to and that those questions adequately cover the areas of interest. The Jump$tart survey completely fails under both criteria.

Temporary Workers

The recent rise in temporary workers is appears to be higher than in previous economic downturns:

This year, 26.2 percent of all jobs added by private sector employers were temporary positions. In the comparable period after the recession of the early 1990s, only 10.9 percent of the private sector jobs added were temporary, and after the downturn earlier this decade, just 7.1 percent were temporary.

Temporary employees still make up a small fraction of total employees, but that segment has been rising steeply over the past year. “It hints at a structural change,” said Allen L. Sinai, chief global economist at the consulting firm Decision Economics. Temp workers “are becoming an ever more important part of what is going on,” he said.

I think that this trend has a couple of features that are worth thinking about. One, it tends to mean that workers will have less institutional knowledge than before. I suppose that there are some employment circumstances where basic skills transfer but one assumes that most workplaces benefit from knowledge of the corporate culture, product knowledge, and so forth.

Second, I think that this trend continues to make the link between employment and benefits health insurance less sustainable. It is unclear if the end game is a government based system, but it sure makes the complexity of constant insurance coverage (without an employer) look like a difficult task.

I am not really sure what the best outcome looks like but I do think that this trend, if it should continue, will bring as many challenges as benefits.

Boom, bust and echo

There is a really nice chart in Worthwhile Canadian Initiative (WCI) about youth unemployment over time (in Canada). I was too young to actually be influenced much by the recession in the 1980's but the recession of the early 1990's (about 6% higher than it is today) dramatically influenced my career trajectory. As a young person, I never imagined that I would end up in the United States.

However, poverty has a way of changing opinions and I headed south for employment reasons. I am struck by how different the tenor of the times was: the articles that were linked to in the WCI post suggest that the issue is greed among those in the older generations. But, back in the day, we were much more likely to hear that young people were unmotivated or spoiled.

I think that we are actually seeing signs of the economic power of young people today that the narrative has shifted so far from what it used to be. But, as a card carrying member of Generation X, I can definitely attest that careers were pushed back and we started a lot later than everyone else simply because jobs were so hard to find.

"What is this 'Canada' of which you speak?"

Following up on Joseph's last post, I remember a discussion about careers I had with a group of friends including Joseph a few years ago. I was looking to make a change and Joseph asked if I'd considered the Canadian term for substitute teaching. I looked at him as though he had suggested I apply for a job scraping roadkill. It took several minutes for him to convince me that where he came from, substitute teaching was actually a sought-after career.

This is consistent with Canada's approach toward teaching in general. Canadians have long worked under the assumption that, if you give teachers security, respect and good salaries, you will attract good teachers. This is just one of the ways that Canada has done the opposite of what education reformers have recommended in this country. Here advocates like Joel Klein and Michelle Rhee insist that without charter schools and the option of mass firings the education system is doomed and yet, by the reformers' own favorite metrics, our northern neighbor consistently kicks our ass.

Demographically, economically, culturally and historically, Canada would seem to be the obvious country to look to when trying to determine the effectiveness of potential U.S. policies but it has been conspicuously absent from a number of debates. Before we start looking across half the world to countries with radically different situations and backgrounds, isn't it possible that we can learn something from a spot closer to home?

Canadian Exceptionalism

Megan McArdle has a comment on whether a social safety net will spur entrepreneurship:

But when we try to look at the net effect, it's hard to see much dynamism coming out of the places with a generous safety net. Rates of entrepreneurship and labor mobility are far lower in Europe than they are in America--and one of the many factors restraining European labor mobility is thought to be the social safety net, both because of the difficulty of moving between benefit system, and because the benefits lessen the urgency of say, relocating in order to find a job.

I will now speak at the level of personal anecdote; I beg the reader’s indulgence but I think it is a worthy point to make. I have lived in both the United States and Canada (as any reader of this blog will probably have figured out). At a purely personal level I am way more comfortable with economic risk when I am resident in Canada.

Why? Because the cost of a hospitalization is so high here in the United States as compared with elsewhere. There are two factors that I think are key. One is simply that medical care is intrinsically expensive here in the United States. But the second is the bargaining power of groups. Look at what the difference is between the billed price and what private insurance pays.

Now imagine that you feel dizzy one day. Dizziness can be a sign of a stroke or a heart attack. But if you are unemployed and not covered then what do you do? Visiting the hospital is a guarantee of some sort of economic crisis. But many events can be stopped with early treatment (or at least highly mitigated).

If we had the features of an efficient market, that would be different. But has anybody ever tried to shop around for better prices in the midst of a serious health event? Yet the United States links health insurance with employment. Furthermore, rescission tends to happen at the time of the event; in cases of gross fraud that is perfectly understandable but the examples of very minor book-keeping errors leading to rescission make one leery of not having somebody (like a large employer's HR department) around to advocate for you. Courts, while possible, are expensive at a time when you likely have no money.

Now this is not to say anything about elective procedures or non-urgent medicine; things like elective eye surgery can be areas that markets can exist. But we can already see this in Canada with things like diagnostic scans (that are not time sensitive) are increasingly handled by private firms in Canada (often paid out of pocket) for a surprisingly low cost to the consumer. The same with laser eye surgery or some forms of bariatric surgery. So a mixed economy is possible.

So I have been a lot more concerned about being employed in stable position here in the United States. In Canada I have considered (and applied for) short term and unstable positions: many of which were a lot more entrepreneurial.

After all, correlating employment risk (i.e. loss of job) with medical care cost risk (when insurance is linked to your job) seems like a bad decision. As for why we don’t see this in Europe – I have no idea. But it’s not clear that the European example is conclusive.

A Christmas Reminder

A lot of people out there have had a rough year so if you're in a position to be generous this is a good time for generosity.

From All Things Considered:

SIEGEL: Joining us from New York City's main post office is head elf, Pete Fontana. He's been working with the U.S. Postal Service Operation Santa for 15 years. Welcome to the program.

Mr. PETE FONTANA (Operation Santa Claus, U.S. Postal Service): Well, thank you for having me.

SIEGEL: And what have you noticed that's different in tone this year about the letters to Santa Claus?

Mr. FONTANA: Well, normally the letters would be what you said, you know, more like greedy-type things - big televisions, Xboxs, Wiis, things of that nature, MacBooks. This year, the letters are single moms, three kids, no winter coats, no shoes, blankets, can't pay the bills, not enough food in the pantry. So the need has changed tremendously.

SIEGEL: Perhaps you can read a couple of those letters to us, Pete.

Mr. FONTANA: Hold on. Here's one from Christopher(ph). Dear Santa, My name is Christopher. I'm 11 years old and I have a sister. Her name is Bethania(ph). She is two years old. And I have a brother who is nine months. If possible, we would like some educational toys and some winter clothes. I would like something to make my mommy happy 'cause she is getting chemotherapy after breast surgery. Something like a hat or a scarf for her. Thank you very much, Christopher.

SIEGEL: Now, your program at the post office is designed to pair children in need with volunteers who might donate gifts. I would imagine that you always see letters like this every year. Is this year really different?

Mr. FONTANA: I would say that this year there just seems to be more needy and less greedy I hate to rhyme it but it just seems that thats what the trend is.

The Homebase study looks OK but the New York Times is still a mess

Alex Tabarrok and Joseph both have posts up on a study to determine the effectiveness of a program to prevent homelessness by randomly accepting 200 of the 400 applicants the program received last summer then comparing how the accepted fare compared to the rejected. This isn't exactly how I'd set the study up but the choices the researchers seem both reasonable and ethical. As one of the researchers pointed out, this was not an entitlement; it is a small program that rejects some applicants already. All the researchers are doing is rearranging the pool.

If everything is as it seems, my only major concern is that, given our current exceptionally bad economic conditions, the results from this study might not generalize well.

But the word 'seems' is important because the NYT story that all of these posts have been based on simply isn't informative enough or well enough written for the reader to manage an informed opinion.

The story starts out ominously with this paragraph:

It has long been the standard practice in medical testing: Give drug treatment to one group while another, the control group, goes without.

Now, New York City is applying the same methodology to assess one of its programs to prevent homelessness. Half of the test subjects — people who are behind on rent and in danger of being evicted — are being denied assistance from the program for two years, with researchers tracking them to see if they end up homeless.

It might not be reasonable to expect a dissertation on the distinction between double-blind and open-label studies, but given that the subject of the article is the effectiveness and ethics of certain kinds of open-label studies, the fact that the writer may not know that there is a distinction does not bode well.

It does, however, bode accurately because the writer apparently proceeds to blur a much more important distinction, that between pilot and ongoing programs:

Such trials, while not new, are becoming especially popular in developing countries. In India, for example, researchers using a controlled trial found that installing cameras in classrooms reduced teacher absenteeism at rural schools. Children given deworming treatment in Kenya ended up having better attendance at school and growing taller.

These are pilot programs. The Indian government didn't install cameras in all their rural schools then go to the expense of randomly removing half of them, nor did the Kenyans suddenly discontinue preventative care from half their children. From a practical, ethical and analytic perspective, going from no one gets a treatment to a randomly selected sample get a treatment is radically different than going from everyone gets a treatment to a randomly selected sample get a treatment.

Putting aside the obvious practical and ethical points, the analytic approach to an ongoing program is different because you start with a great deal of data. You don't have to be a Bayesian to believe that data from other sources should affect the decisions a statistician makes, choices ranging from prioritizing to deciding what to study to designing experiments. Statisticians never work in a vacuum.

There is little doubt that the best data on this program that we could reasonably hope for would come from some kind of open-label study with random assignment but, given the inevitable concerns and caveats that go with open-label studies, exactly how much better would that data be? What kind of data came out the original pilot study? What kind of data do we have on similar programs across the country? And most importantly, what's the magnitude of the effect we seem to be seeing?

On that topic we get the following piece of he said/she said:

Advocates for the homeless said they were puzzled about why the trial was necessary, since the city proclaimed the Homebase program as “highly successful” in the September 2010 Mayor’s Management Report, saying that over 90 percent of families that received help from Homebase did not end up in homeless shelters.

...

But Seth Diamond, commissioner of the Homeless Services Department, said that just because 90 percent of the families helped by Homebase stayed out of shelters did not mean it was Homebase that kept families in their homes. People who sought out Homebase might be resourceful to begin with, he said, and adept at patching together various means of housing help.

Before we can ask if this proposed selection effect can explain the impact of Homebase, it would help if we had the slightest idea what that impact was. It's true that over 90 percent of the families in question did not end up in shelters. It is also true that 99.99 percent of the people who took homeopathic remedies for their colds did recover. Neither number is particularly useful without the proper context.

The proper context shouldn't be that difficult to find. We have more than enough information to estimate the likelihood of families in these financial situations ending up in shelters. Of course, there is no upper bound on a possible selection effect, but I'm going to weight the possibility differently if the comparison rate turns out to be 80 percent than I would if it were 40 percent.

None of this is a criticism of the actual research. Other than my concern about generalizing 2010 economic data, this looks like a good study. Governments and large organizations should always be on the lookout for ways that experimental design and sampling theory can improve our data.

But I can't say with any certainty that this is a good place for this kind data gathering because I'm getting my information from a badly written story. There are three papers I read frequently: the LA Times, the New York Times and the Wall Street Journal, and of those, the one that is most likely to run lazy, low-context, he said/she said pieces is the old gray lady.

Merit?

From the comments section of Worthwhile Canadian Initiative:

Actually one of my favourite questions on the 2008 US Jump$tart survey is this one:

Don and Bill work together in the finance department of the same company and earn the same pay. Bill spends his free time taking work-related classes to improve his computer skills; while Don spends his free time socializing with friends and working out at a fitness center. After five years, what is likely to be true?

a) Don will make more because he is more social.
b) Don will make more because Bill is likely to be laid off.
c) Bill will make more money because he is more valuable to his company.*
d) Don and Bill will continue to make the same money.

Not at all obvious to me that (c) is the right answer.

[Note: the * next to (c) indicates that it is the correct answer for the key.] I can certainly think of examples where this answer would seem to be contradicted by empirical reality. And that is before one worried about outsourcing or what happens if the company completely changes software platforms in a major re-org.

The post and comments are worth reading, throughout.

Randomized Social Experiments

In a really fascinating post, Alex Tabarrok discusses controversy about a random clinical trial set within a housing program. It's a very interesting example (and his quote from E. E. Peacock, Jr. was priceless). But it does bring up a serious question: in many areas of social policy there is no realistic way to blind experiments and, similarly, the idea of informed consent is hard to implement in practice.

Consider this point as well: the only way you will be able to get rational actors to consent to an experiment on housing is if all of the options in the intervention are equal or better than the status quo. That means you can never experiment to see if the current plans are working, insofar as informed consent is required. Nor can one really argue that coercion is not present given that people enter these programs out of desperation.

I think the real difference is that we have two different sources of utility: the user of the program and the agency (via the taxpayer) who is implementing the program. So it becomes a complex problem because the status quo might benefit the user (marginally) and harm the taxpayer/state/agency (greatly) but you will never get users to consent to testing how they will do with fewer benefits (or at least the incentives are wrong). Compare this with drug trials: only the patient’s ability to benefit is typically considered (although cost effectiveness may matter later in the approval process).

But the alternative is simply to not know what the right answer is and to risk getting stuck at a very suboptimal policy point. And that seems to be the wrong answer as well.

"I am not now and have never been a constructionist"

(This post also appears at Education and Statistics.)

After my last post thought I should run this titular disclaimer. For those of you not up on the subject, here's a definition from the well-written Wikipedia entry on the subject:

Constructivist teaching is based on constructivist learning theory. This theoretical framework holds that learning always builds upon knowledge that a student already knows; this prior knowledge is called a schema. Because all learning is filtered through pre-existing schemata, constructivists suggest that learning is more effective when a student is actively engaged in the learning process rather than attempting to receive knowledge passively. A wide variety of methods claim to be based on constructivist learning theory. Most of these methods rely on some form of guided discovery where the teacher avoids most direct instruction and attempts to lead the student through questions and activities to discover, discuss, appreciate and verbalize the new knowledge.

Don't get me wrong. For the right topic, executed the right way with the right teacher and class, this can be a great, wonderful, spectacular and really good approach to education. Unfortunately, education reformers (particularly the current crop), are not good at conditional problems. They tend instead to fall into the new tool camp (you know the saying, "to a man with a new hammer, the whole world is a nail.").

Worse yet, (and I'm afraid there's no nice way to say this) many of the educational theorists don't have a firm grasp on the subjects they are working with. This is never more plain than in constructionist science classes that almost entirely eschew lectures and traditional reading assignments and instead have the students spend their time conducting paint-by-numbers experiments, recording the results and performing a few simple calculations.

To most laymen, that's what science is: stuff you do while wearing a lab coat. Most people don't associate science with forming hypotheses, designing experiments, analyzing results and writing papers and, based on my limited but first hand experience, many science educators don't give those things much thought either.

The shining exception to the those-who-can't-teach-teach-teachers rule is George Polya. Though best known as an educational theorist, Polya was a major Twentieth Century mathematician (among his other claims to fame, he coined the term "central limit theorem") so he certainly fell in the those-who-can camp.

But it it important to note that Polya advocated guided discovery specifically as a way of teaching the problem solving process. I suspect that when it came to simply acquiring information, he would have told his students to go home and read their textbooks.

"Reasons to teach what we teach"

I've got a long post up on Education and Statistics on the reasons for including a concept in the mathematics curriculum and how those reasons should affect what we teach and how we teach it.

Here's an excerpt:

Where a topic appears on this list affects the way it should be taught and tested. Memorizing algorithms is an entirely appropriate approach to problems that fall primarily under number one [Needed for daily life]. Take long division. We would like it if all our students understood the underlying concepts behind each step but we'll settle for all of them being able to get the right answer.

If, however, a problem falls primarily under four [helps develop transferable skills in reasoning, pattern-recognition and problem-solving skills], this same approach is disastrous. One of my favorite examples of this comes from a high school GT text that was supposed to develop logic skills. The lesson was built around those puzzles where you have to reason out which traits go with which person (the man in the red house owns a dog, drives a Lincoln and smokes Camels -- back when people in puzzles smoked). These puzzles require some surprisingly advanced problem solving techniques but they really can be enjoyable, as demonstrated by the millions of people who have done them just for fun. (as an added bonus, problems very similar to this frequently appear on the SAT.)

The trick to doing these puzzles is figuring out an effective way of diagramming the conditions and, of course, this ability (graphically depicting information) is absolutely vital for most high level problem solving. Even though the problem itself was trivial, the skill required to find the right approach to solve it was readily transferable to any number of high value areas. The key to teaching this type of lesson is to provide as little guidance as possible while still keeping the frustration level manageable (one way to do this is to let the students work in groups or do the problem as a class, limiting the teacher's participation to leading questions and vague hints).

What you don't want to do is spell everything out and that was, unfortunately, the exact approach the book took. It presented the students with a step-by-step guide to solving this specific kind of logic problem, even providing out the ready-to-fill-in chart. It was like taking the students to the gym then lifting the weights for them.

This is a bit of a work in progress so if you have any relevant experience in mathematics education (and, yes, experience as a student definitely counts), I would greatly appreciate it if you went by and joined the conversation.

Interesting Passage

Via Tyler Cowen of Marginal Revolution fame comes an interesting article on school choice. I was particularly struck by this passage:

This approach helps explain why choice advocates — inclined to approach choice-based reform not as a regulatory question, but as one of justice and rights — have spent so much less time considering the dynamics of deregulation than have pro-market reformers in sectors like transportation, telecommunications, and cable television. Because education reformers have approached choice not as a matter of political economy but as a moral crusade, they have favored grand, sweeping claims over empirical reality.

I think that this has a lot of explanatory power for the postive treatment that charter schools are getting in the press and among pundits. Mark has written about this extensively on this blog.

I think breaking apart the moral and the policy dimensions would be a positive development. The issues with under-servicing of some groups are broad but there is a risk that alternatives could make things worse.