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Most of us think that we are “better than average” in most things. We are also “miscalibrated,” meaning that our sense of the probability of events doesn’t line up with reality. When we say we are sure about a certain fact, for example, we may well be right only half the time.

Some economists have questioned whether such experimental findings are relevant in competitive markets. They suggest that students, who often serve as guinea pigs in such tests, are overconfident, but that the top managers in large companies are well calibrated. A recent paper, however, reveals that this hopeful view is itself overconfident.

“Bilingualism carries a cost, and the cost is rapid access to words,” Ms. Bialystok said. In other words, children have to work harder to access the right word in the right language, which can slow them down — by milliseconds, but slower nonetheless.

At the same time, bilingual children do better at complex tasks like isolating information presented in confusing ways. In one test researchers frequently use, words like “red” and “green” flash across a screen, but the words actually appear in purple and yellow. Bilingual children are faster at identifying what color the word is written in, a fact researchers attribute to a more developed prefrontal cortex (the part of the brain responsible for executive decision-making, like which language to use with certain people). Ms. D’Souza said that both of her sons lagged their peers by almost a year in verbal development. Her pediatrician recommended speech therapy, and one son’s preschool teacher expressed concern that he did not know the alphabet. But when both started speaking, at around 3 years old, they were able to move fluidly among three languages. She said that her older son tested in the 99th percentile for the city’s gifted and talented program. “The flexibility of their thinking helps them in nonlinguistic abilities like science and math,” she said, speaking of her children. “But at the same time the normal things — the alphabet — they have trouble with that.”

George P. Davison, head of school at Grace Church School, a competitive downtown school, said that bilingualism tended to suppress verbal and reading comprehension test scores by 20 to 30 percent for children younger than 12. “If anything, it can have a negative effect on admissions,” he said.

In their book “Grand Theft Childhood,” the authors Lawrence Kutner and Cheryl K. Olson of Harvard Medical School argue that this causal claim is only the result of “bad or irrelevant research, muddleheaded thinking and unfounded, simplistic news reports,.”

This fall, the U.S. Supreme Court will rule on a case that may have the unusual result of establishing a philosophical link between Arnold Schwarzenegger and Plato. The case in question is the 2008 decision of the Ninth Circuit Court of Appeals striking down a California law signed by Gov. Schwarzenegger in 2005, that imposed fines on stores that sell video games featuring “sexual and heinous violence” to minors.  The issue is an old one: one side argues that video games shouldn’t receive First Amendment protection since exposure to violence in the media is likely to cause increased aggression or violence in real life.  The other side counters that the evidence shows nothing more than a correlation between the games and actual violence.

To begin with, he accuses it of conflating the authentic and the fake.  Its heroes appear genuinely admirable, and so worth emulating, although they are at best flawed and at worst vicious.  In addition, characters of that sort are necessary because drama requires conflict — good characters are hardly as engaging as bad ones.  Poetry’s subjects are therefore inevitably vulgar and repulsive — sex and violence.  Finally, worst of all, by allowing us to enjoy depravity in our imagination, poetry condemns us to a depraved life. Both Plato and Arnheim ignored the medium of representation, which interposes itself between the viewer and what is represented. This very same reasoning is at  the heart of today’s denunciations of mass media.  Scratch the surface of any attack on the popular arts — the early Christians against the Roman circus, the Puritans against Shakespeare, Coleridge against the novel, the various assaults on photography, film, jazz, television, pop music, the Internet, or video games — and you will find Plato’s criticisms of poetry.  For the fact is that the works of  both Homer and Aeschylus, whatever else they were in classical Athens, were, first and  foremost, popular entertainment.

In 1935, Rudolf Arnheim called television “a mere instrument of transmission, which does not offer any new means for the artistic representation of reality.”  He was repeating, unawares, Plato’s ancient charge that, without a “craft” or an art of his own, Homer merely reproduces “imitations,” “images,” or “appearances” of virtue and, worse, images of vice masquerading as virtue.  Both Plato and Arnheim ignored the medium of representation, which interposes itself between the viewer and what is represented.

But what about us?  Do we, as Plato thought, move immediately from representation to reality?  If we do, we should be really worried about the effects of television or video games.  Or are we aware that many features of each medium belong to its conventions and do not represent real life?

There is a large leap, however, between having data and learning from it. Students need to know the potential of number-crunching, as well as its limitations.

Economists like me often pretend that people are rational. That is, with mathematical precision, people are assumed to do the best they can to achieve their goals.

or many purposes, this approach is useful. But it is only one way to view human behavior. A bit of psychology is a useful antidote to an excess of classical economics. It reveals flaws in human rationality, including your own.

I don’t know if it made me a better economist. But it has surely made me a more humble one, and, I suspect, a better human being as well.

Adults of all stripes have advice for the college-bound. Those leaving home and starting their freshman year should listen to it, consider it, reflect on it but ultimately follow their own instincts and passions.

But at the very least, the cognitive techniques give parents and students, young and old, something many did not have before: a study plan based on evidence, not schoolyard folk wisdom, or empty theorizing.

“With many students, it’s not like they can’t remember the material” when they move to a more advanced class, said Henry L. Roediger III, a psychologist at Washington University in St. Louis. “It’s like they’ve never seen it before.”

That’s one reason cognitive scientists see testing itself — or practice tests and quizzes — as a powerful tool of learning, rather than merely assessment. The process of retrieving an idea is not like pulling a book from a shelf; it seems to fundamentally alter the way the information is subsequently stored, making it far more accessible in the future.

Dr. Roediger uses the analogy of the Heisenberg uncertainty principle in physics, which holds that the act of measuring a property of a particle (position, for example) reduces the accuracy with which you can know another property (momentum, for example): “Testing not only measures knowledge but changes it,” he says — and, happily, in the direction of more certainty, not less.

“Testing has such bad connotation; people think of standardized testing or teaching to the test,” Dr. Roediger said. “Maybe we need to call it something else, but this is one of the most powerful learning tools we have.”

Motivation matters. So do impressing friends, making the hockey team and finding the nerve to text the cute student in social studies.

The more mental sweat it takes to dig it out, the more securely it will be subsequently anchored.

“In lab experiments, you’re able to control for all factors except the one you’re studying,” said Dr. Willingham. “Not true in the classroom, in real life. All of these things are interacting at the same time.”

they directly contradict much of the common wisdom about good study habits, and they have not caught on.

“Instead, we walk around with all sorts of unexamined beliefs about what works that are mistaken.”

“The contrast between the enormous popularity of the learning-styles approach within education and the lack of credible evidence for its utility is, in our opinion, striking and disturbing,” the researchers concluded.

“We have yet to identify the common threads between teachers who create a constructive learning atmosphere,”

psychologists have discovered that some of the most hallowed advice on study habits is flat wrong. For instance, many study skills courses insist that students find a specific place, a study room or a quiet corner of the library, to take their work. The research finds just the opposite. In one classic 1978 experiment, psychologists found that college students who studied a list of 40 vocabulary words in two different rooms — one windowless and cluttered, the other modern, with a view on a courtyard — did far better on a test than students who studied the words twice, in the same room. Later studies have confirmed the finding, for a variety of topics.

The brain makes subtle associations between what it is studying and the background sensations it has at the time, the authors say, regardless of whether those perceptions are conscious. It colors the terms of the Versailles Treaty with the wasted fluorescent glow of the dorm study room, say; or the elements of the Marshall Plan with the jade-curtain shade of the willow tree in the backyard. Forcing the brain to make multiple associations with the same material may, in effect, give that information more neural scaffolding.