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Archive for the ‘Teaching’ Category

You’ve probably seen recent reports that low-income, high-achieving high school students set their college sights much lower than their high-income counterparts. That’s the chief finding of recent research by Stanford’s Caroline M. Hoxby and Harvard’s Christopher Avery presented last week at Brookings Papers on Economic Activity.

That finding is nicely illustrated in an infographic accompanying the paper (click for a higher-resolution version):

hoxby02

Here’s their summary of findings:

We show that the vast majority of very high-achieving students who are low-income do not apply to any selective college or university. This is despite the fact that selective institutions would often cost them less, owing to generous financial aid, than the resource-poor two-year and non-selective four-year institutions to which they actually apply. Moreover, high-achieving, low-income students who do apply to selective institutions are admitted and graduate at high rates. We demonstrate that these low-income students’ application behavior differs greatly from that of their high-income counterparts who have similar achievement. The latter group generally follows the advice to apply to a few “par” colleges, a few “reach” colleges, and a couple of “safety” schools. We separate the low-income, high-achieving students into those whose application behavior is similar to that of their high-income counterparts (“achievement-typical” behavior) and those whose apply to no selective institutions (“income-typical” behavior). We show that income-typical students do not come from families or neighborhoods that are more disadvantaged than those of achievement-typical students. However, in contrast to the achievement-typical students, the income-typical students come from districts too small to support selective public high schools, are not in a critical mass of fellow high achievers, and are unlikely to encounter a teacher or schoolmate from an older cohort who attended a selective college. We demonstrate that widely-used policies–college admissions staff recruiting, college campus visits, college access programs–are likely to be ineffective with income-typical students, and we suggest policies that will be effective must depend less on geographic concentration of high achievers.

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My Sunday reading turned up three examples of glaring numeracy errors. I make plenty of my own errors, so I have sympathy for the perpetrators. But I did want to highlight them as examples of what can happen when quantitative thinking runs off the rails. And the need to remain mathematically vigilant in your daily life.

So please take this short numeracy quiz. My answers after the fold.

1. How much has teen drinking declined?

In today’s New York Times Magazine, Tara Parker-Pope makes the case that teenagers are more conservative than their parents were. For example, the fraction of high-school seniors who reported that they had recently consumed alcohol fell from 72% in 1980 to 40% in 2011.

I have no beef with those statistics (or that trend), but I do wonder about the chart used to illustrate it. Do you see anything wrong in this visual?

2. What’s a fair way for students to hedge their bets on today’s Super Bowl?

A few pages later (in the ink-and-paper edition), the NYT’s Ethicist, Ariel Kaminer receives a letter from a parent whose child was offered a bet on the Super Bowl … by their school. Leaving aside the propriety of book-making in the class room, what do you think of this wager?

My school charged a dollar for students to bet, or “predict,” which team would win the Super Bowl. It was $1 for one team, and if you won, you would get a candy bar. If you bet $3, you could choose both teams and guarantee your candy bar. Is this legal or even morally right?

3. How much does federal compensation exceed private compensation?

In Friday’s Wall Street Journal, finally, Steve Moore makes the case that federal workers are overpaid. What’s wrong in the following excerpt? (ht: Brad DeLong)

Federal workers on balance still receive much better benefits and pay packages than comparable private sector workers, the Congressional Budget Office reports. The report says that on average the compensation paid to federal workers is nearly 50% higher than in the private sector, though even that figure understates the premium paid to federal bureaucrats.

CBO found that federal salaries were slightly higher (2%) on average, while benefits — including health insurance, retirement and paid vacation — are much more generous (48% higher) than what same-skilled private sector workers get.

(more…)

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Last week, I noted that former Stanford professor Sebastian Thrun enrolled 160,000 students in an online computer science class. That inspired him to set up a new company, Udacity, to pursue online education. A new article in Bloomberg BusinessWeek adds some additional color to the story.

Barrett Sheridan and Brendan Greeley answer a question many folks asked about the students: how many actually finished? Answer: 23,000 finished all the assignments.

Second, they note that professor Thrun is also at the forefront of another potentially transformative technology: self-driving cars:

Last fall, Stanford took the idea further and conducted two CS courses entirely online. These included not just instructional videos but also opportunities to ask questions of the professors, get homework graded, and take midterms—all for free and available to the public.

Sebastian Thrun, a computer science professor and a Google fellow overseeing the search company’s project to build driverless cars, co-taught one of the courses, on artificial intelligence. It wasn’t meant for everyone; students were expected to get up to speed with topics like probability theory and linear algebra. Thrun’s co-teacher, Peter Norvig, estimated that 1,000 people would sign up. “I’m known as a crazy optimist, so I said 10,000 students,” says Thrun. “We had 160,000 sign up, and then we got frightened and closed enrollment. It would have been 250,000 if we had kept it open.” Many dropped out, but 23,000 students finished all 11 weeks’ worth of assignments. Stanford is continuing the project with an expanded list of classes this year. Thrun, however, has given up his tenured position to focus on his work at Google and to build Udacity, a startup that, like Codecademy, will offer free computer science courses on the Web.

I wish Thrun success in both endeavors. Perhaps one day soon, commuters will settle in for an hour of online learning while their car drives them to work.

P.S. In case you missed it, Tom Vanderbilt has a fun article on self-driving cars in the latest Wired.

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That’s what former Stanford professor Sebastian Thrun aims to do.

Sound impossible? Well, he’s already taught a class of 160,000 students. As Felix Salmon recounts:

Thrun told the story of his Introduction to Artificial Intelligence class, which ran from October to December last year. It started as a way of putting his Stanford course online — he was going to teach the whole thing, for free, to anybody in the world who wanted it. With quizzes and grades and a final certificate, in parallel with the in-person course he was giving his Stanford undergrad students. He sent out one email to announce the class, and from that one email there was ultimately an enrollment of 160,000 students. Thrun scrambled to put together a website which could scale and support that enrollment, and succeeded spectacularly well.

Just a couple of datapoints from Thrun’s talk: there were more students in his course from Lithuania alone than there are students at Stanford altogether. There were students in Afghanistan, exfiltrating war zones to grab an hour of connectivity to finish the homework assignments. There were single mothers keeping the faith and staying with the course even as their families were being hit by tragedy. And when it finished, thousands of students around the world were educated and inspired. Some 248 of them, in total, got a perfect score: they never got a single question wrong, over the entire course of the class. All 248 took the course online; not one was enrolled at Stanford.

And I loved as well his story of the physical class at Stanford, which dwindled from 200 students to 30 students because the online course was more intimate and better at teaching than the real-world course on which it was based.

 Inspired by that experience, Thrun has now founded Udacity, a private online university. As Nick DeSantis of the Chronicle of Higher Education reports:

One of Udacity’s first offerings will be a seven-week course called “Building a Search Engine.” It will be taught by David Evans, an associate professor of computer science at the University of Virginia and a Udacity partner. Mr. Thrun said it is designed to teach students with no prior programming experience how to build a search engine like Google. He hopes 500,000 students will enroll.

Teaching the course at Stanford, Mr. Thrun said, showed him the potential of digital education, which turned out to be a drug that he could not ignore.

“I feel like there’s a red pill and a blue pill,” he said. “And you can take the blue pill and go back to your classroom and lecture your 20 students. But I’ve taken the red pill, and I’ve seen Wonderland.”

That Wonderland will be a serious challenge to traditional chalk-and-talk universities — and a wonderful opportunity to democratize knowledge around the globe.

(ht: Alex Tabarrok at Marginal Revolution)

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That’s the question that Jeffrey Selingo poses over the The Chronicle of Higher Education (ht: Jack B.):

[I]f current economic trends continue, much of traditional academe is going to be forced to change. Families can no longer use their house as an ATM. States are making tough choices about the size of government, and public colleges are often left at the end of the line. And now the federal government is likely to cut back on many of its fiscal promises to deal with an out-of-control deficit.

The bottom line is that we’re likely to face a future where students and their families pay a lot more of the cost of a college education out of pocket. Without grants and loans as a safety net, students are probably going to make different choices than they do now (read: less expensive choices). We’re likely headed toward a future where smaller, struggling colleges need to move to new models of doing business, while elite, wealthy colleges continue to support the current model.

Selingo then summarizes several ideas that were bandied about in a meeting of academic “disruptors” and disruptive innovation guru Clayton Christensen of Harvard Business School. They include:

  • Disaggregated universities, in which colleges would purchase courses from other colleges (or, I suppose, sources like Khan Academy) rather than produce them themselves, and
  • Modular universities, in which colleges would provide much more focused degree offerings.

Also on the agenda: rethinking the often-anachronistic academic year and the scholastic currency known as the credit hour.

To be sure, none of these ideas are particularly earth-shattering. But that may well be the larger point. America’s higher education “industry” might well reap substantial benefits from adopting organizational ideas that are already old hat elsewhere in the economy.

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At last Wednesday’s hearing on tax reform, three witnesses–Rosanne Altshuler, Larry Lindsey, and I–invoked a famous rule of thumb about taxes. We each told the Senate Budget Committee that high tax rates are disproportionately harmful for the economy and that:

If you double tax rates, you quadruple the resulting economic harm.

If a 10% tax rate on some activity does a certain amount of economic damage, for example, then it’s a reasonable guess that doubling the tax rate to 20% would multiply that damage by a factor of four.

It was nice to hear such agreement among the panelists, but judging by the senators’ reaction, this idea is not intuitive. So let me try to explain with a simple example.

Suppose there are five people who might buy a pizza. The first person values a pizza at $14.50, the second at $13.50, the third at $12.50, the fourth at $11.50, and the fifth at $10.50.

If pizzas cost $10, all five people will buy one. The first person gets a net benefit of $4.50, since the pizza was worth $14.50 to her, but she paid only $10. The second person gets a benefit of $3.50, and so on. Add it all up, and the benefit of the pizza market is $12.50 (= $4.50 + $3.50 + $2.50 + $1.50 + $0.50).

Now suppose that the government levies a 10% tax on pizzas; that lifts the price to $11. Now only the four consumers who place the highest value on pizzas will buy them; Mr. $10.50 won’t buy. The four remaining consumers now benefit by $3.50 + $2.50 + $1.50 + $0.50 = $8.00 from buying pizza. The government collects $4.00 in revenue, so the total economic benefit of the pizza market is $12.00, $0.50 less than before. That 50-cent loss falls on the hungry guy who no longer buys a pizza. The $1 loss for each of the four buyers isn’t lost to the economy; instead, it transfers to the government.

Now suppose, instead, that the tax is 20%; pizzas now cost $12 each, and only three consumers will buy. Their total benefit is $4.50 (= $2.50 + $1.50 + $0.50). The government collects $6.00 in revenue, so the total economic benefit is $10.50. That’s $2.00 less than without a tax.

So there you have it. When you double the tax from 10% to 20%, you quadruple the economic harm from $0.50 to $2.00.

Why does this happen? Because doubling the tax doubles the number of consumers who drop out (from 1 to 2) and doubles the average economic value of the pizza sales that never happen (from $0.50 to $1.00). Two times two is four, so the overall effect is to quadruple the economic harm.

Put another way, the value of the second lost pizza ($1.50) is three times larger than the value of the first one ($0.50). So the economic harm of the 20% tax is four times the harm of the 10% tax.

This is a big deal when you design a tax system for the entire economy. To avoid needless economic harm, you should aim for low tax rates and the broadest possible tax base. If you need to raise $6.00 from our mythical food economy, for example, it would be far better to levy a 5% tax on pizzas, tacos, and hamburgers, than a 20% tax on pizzas alone.

I hope that whets your appetite for base-broadening tax reform.

P.S. Did I cook the pizza example to get the increase to be exactly a factor of four? Of course. In the real world, the actual multiple will vary. If the fifth person valued the pizza at only $10.25, for example, the loss from the 10% tax would have been $0.25, and the loss from the 20% tax would have been seven times larger at $1.75. Conversely, if the fourth person valued the pizza at only $11.00, the loss from the 20% tax would have been $1.50, only three times larger than the $0.50 loss from the 10% tax. The double/quadruple rule of thumb assumes an even spread of consumers and their values — a reasonable starting assumption until you have more information.

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Earlier in the semester, my students bravely endured the usual microeconomic approach to understanding consumer choice. You know: budget constraints, indifference curves, and tangencies. Very useful when deployed appropriately, but rather abstract.

To lighten things up—and illustrate some important truths about how consumers actually behave—we then spent a class on the psychology / behavioral economics of consumer choice.

For me, the most fun part was discussing menu engineering. In the usual economic model, people make choices based on prices and the attributes of the goods they can buy. Those things matter in the real world too, but consumers are also influenced by other information. For example, their purchase decisions can sometimes be steered by crafty decisions about what options to include on the menu.

One good example is Dan Ariely’s now-famous experiment with subscription rates for The Economist magazine. In one experiment, his students were offered the choice between paying $59 per year for an online subscription or $125 for print plus online. In a second experiment, they were offered three choices: $59 for an online subscription, $125 for a print subscription, or $125 for a print/online subscription.

Standard economic analysis suggests that the print-only option in the second experiment shouldn’t matter. No one should choose it since they could get print+online for the same price. In practical terms, then, the comparison is the same as the first experiment: online at $59 or print+online at $125. And so standard economics would predict that consumers would make the same choices in the two experiments.

That’s not the way it worked out. In the first experiment, 68% of his students chose the online edition of The Economist and 32% went for print+online. In the second experiment, however, 84% went for print+online, while only 16% went for the online. The good news for standard economics is that no one chose print only. The bad news is that including that option had a big effect on choices. Even though people didn’t want that option, it made the other $125 option look more attractive. In short, it established a reference from which people might decide that the $125 print+online choice was a bargain. So many more of them chose it.

Retailers have understood this psychology for years, of course, while economists are just catching up. But growing interest in behavioral economics has also spawned further innovation in retail, and we are seeing the rise of a new species of consultant: the menu engineer.

Menu engineers advise restaurants and other retailers how to design their menus to encourage customers to buy more and to steer them to more profitable purchases. Consistent with The Economist example, one standard piece of advice is including high-priced items just to make everything else look like a bargain. Menu engineers also recommend that restaurants not use dollar signs; people spend more when they aren’t reminded it’s money. And then there’s a whole science to writing the mouth-watering prose describing each item.

If you have a few minutes, this Today Show interview with a menu engineer is quite amusing.

And for a guided tour of menu tricks, see this piece in New York magazine (ht: Tyler Cowen).

P.S. For completeness, I should note that, according to the Economist entry linked above, the Economist stopped using the three-part pricing system. So maybe it doesn’t work as well in the real world as Ariely’s experiments suggest.

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