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75 percent of young Americans, between the ages of 17 to 24, are unable to enlist in the military today because they have failed to graduate from high school, have a criminal record, or are physically unfit.

Tony Wagner, the Harvard-based education expert and author of “The Global Achievement Gap,” explains it this way. There are three basic skills that students need if they want to thrive in a knowledge economy: the ability to do critical thinking and problem-solving; the ability to communicate effectively; and the ability to collaborate.

Wagner thinks we should create a West Point for teachers: “We need a new National Education Academy, modeled after our military academies, to raise the status of the profession and to support the R.& D. that is essential for reinventing teaching, learning and assessment in the 21st century.”

Richard Ludlow started the nonprofit Academic Earth two years ago after M.I.T.'s OpenCourseWare helped him pass linear algebra as a Yale undergraduate. His site offers the courses of 10 elite universities — 130 full courses and more than 3,500 video lectures. Viewers can turn the tables on professors and grade courses. Other guidance includes "Editor's Picks" and "Playlists," lectures selected around a theme like "First Day of Freshman Year" and "You Are What You Eat."

Connexions, started at Rice University 10 years ago, debundles education for the D.I.Y. learner. Anyone can write a "module," the term for instructional material that can be a single sentence or 1,000 pages. Connexions hosts more than 16,000 modules that make up almost 1,000 "collections." A collection might be, say, an algebra textbook or statistics course.

Daniel Colman is a curator of sorts. He sifts through the vast amount of free courses, movies and books offered online to find what he considers the very best in content and production value. Then he features them on Open Culture, the Web site he founded in 2006. It's a task in keeping with his mission as associate dean and director of Stanford's continuing education program.

the assumption that there is a single established body of mathematical skills that everyone needs to know to be prepared for 21st-century careers. This assumption is wrong. The truth is that different sets of math skills are useful for different careers, and our math education should be changed to reflect this fact.

Today, American high schools offer a sequence of algebra, geometry, more algebra, pre-calculus and calculus (or a “reform” version in which these topics are interwoven). This has been codified by the Common Core State Standards, recently adopted by more than 40 states. This highly abstract curriculum is simply not the best way to prepare a vast majority of high school students for life.

A math curriculum that focused on real-life problems would still expose students to the abstract tools of mathematics, especially the manipulation of unknown quantities. But there is a world of difference between teaching “pure” math, with no context, and teaching relevant problems that will lead students to appreciate how a mathematical formula models and clarifies real-world situations.

Hispanics made up 16 percent of America’s population in 2009, but that is forecast to surge to 29 percent by 2050

Spanish is easy enough that kids really can emerge from high school with a very useful command of the language that they will retain for life, while Mandarin takes about four times as long to make the same progress.

In effect, Chinese is typically a career. Spanish is a practical add-on to your daily life, meshing with whatever career you choose.

The price valued the digital pin board company, which lets people save images and links from around the web, at $12.7 billion. That is a little above its last private fund-raising round, which had pegged the company at $12 billion.By selling at $19 a share, Pinterest raised $1.6 billion from big investors

In its I.P.O. prospectus, Pinterest emphasized its differences from some of those services. Pinterest is not a social media app for hanging out with celebrities or broadcasting one’s life, the company said. It is meant to be personal. The company’s 250 million monthly active users, called “pinners,” come to the site to plan their lives, including home projects, weddings and meals.

The brain, it seems, does not make much of a distinction between reading about an experience and encountering it in real life; in each case, the same neurological regions are stimulated. Keith Oatley, an emeritus professor of cognitive psychology at the University of Toronto (and a published novelist), has proposed that reading produces a vivid simulation of reality, one that “runs on minds of readers just as computer simulations run on computers.” Fiction — with its redolent details, imaginative metaphors and attentive descriptions of people and their actions — offers an especially rich replica. Indeed, in one respect novels go beyond simulating reality to give readers an experience unavailable off the page: the opportunity to enter fully into other people’s thoughts and feelings.

Early this year, Mr. Chetty and five other researchers set out to fill this void. They examined the life paths of almost 12,000 children who had been part of a well-known education experiment in Tennessee in the 1980s. The children are now about 30, well started on their adult lives.

Just as in other studies, the Tennessee experiment found that some teachers were able to help students learn vastly more than other teachers. And just as in other studies, the effect largely disappeared by junior high, based on test scores. Yet when Mr. Chetty and his colleagues took another look at the students in adulthood, they discovered that the legacy of kindergarten had re-emerged.

The rankings stem from a desire by policy makers to find an objective way to distinguish between effective and ineffective teachers, untainted by the subjective judgment of individual evaluators, like school principals.

Critics also say there are aspects of a child’s life — or distractions on test day — that the numbers cannot capture: supportive parents, a talented principal, the help of a tutor, allergies or a relentlessly barking dog outside the classroom.

there are schools where students are taught by multiple teachers, making it difficult to figure out the weight of their individual contributions

What I was doing was perfectly legal. In North Carolina, long-gun transfers by private sellers require no background checks.