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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.

these economists are selling teenagers short

adolescence, like early childhood, is a “period of tremendous ‘neuroplasticity,

“It’s friendship and pushing — they nag them to success,”

Dr. Mason, who teaches economics at the University of North Florida, believes his students are just as intelligent as they’ve always been. But many of them don’t read their textbooks, or do much of anything else that their parents would have called studying. “We used to complain that K-12 schools didn’t hold students to high standards,” he says with a sigh. “And here we are doing the same thing ourselves.”

all evidence suggests that student disengagement is at its worst in Dr. Mason’s domain: undergraduate business education.

“Business education has come to be defined in the minds of students as a place for developing elite social networks and getting access to corporate recruiters,”

Economists are trying to measure a home computer’s educational impact on schoolchildren in low-income households.

little or no educational benefit is found. Worse, computers seem to have further separated children in low-income households, whose test scores often decline after the machine arrives, from their more privileged counterparts.

few children whose families obtained computers said they used the machines for homework. What they were used for — daily — was playing games.

Only one or two students out of every 100 displayed the level of science mastery that the department defines as advanced

a smaller proportion of American 12th graders demonstrated proficiency in science than in any other subject that the federal government has tested since 2005 — except history

Twenty-one percent of the nation’s 12th graders scored at or above the proficient level in science on the 2009 tests, compared with 42 percent who demonstrated proficiency on the most recent economics exam, and 38 percent and 26 percent, respectively, on the most recent nationwide reading and math tests.

“The course is really a refresher, but they aren’t ready for a refresher. They need to learn how to learn.”

The knowledge gap at community colleges is increasingly being recognized as a national problem.

“Many, many community college presidents will say that math developmental education is the most difficult problem they’re facing,”

The studying that middle school and high school students do after the dismissal bell rings is either an unreasonable burden or a crucial activity that needs beefing up. Which is it? Do American students have too much homework or too little? Neither, I’d say. We ought to be asking a different question altogether. What should matter to parents and educators is this: How effectively do children’s after-school assignments advance learning?

The quantity of students’ homework is a lot less important than its quality. And evidence suggests that as of now, homework isn’t making the grade. Although surveys show that the amount of time our children spend on homework has risen over the last three decades, American students are mired in the middle of international academic rankings: 17th in reading, 23rd in science and 31st in math, according to results from the Program for International Student Assessment released last December.

“Spaced repetition” is one example of the kind of evidence-based techniques that researchers have found have a positive impact on learning. Here’s how it works: instead of concentrating the study of information in single blocks, as many homework assignments currently do — reading about, say, the Civil War one evening and Reconstruction the next — learners encounter the same material in briefer sessions spread over a longer period of time. With this approach, students are re-exposed to information about the Civil War and Reconstruction throughout the semester.

When it comes to showing results, he said, “We better put up or shut up.”

Critics counter that, absent clear proof, schools are being motivated by a blind faith in technology and an overemphasis on digital skills — like using PowerPoint and multimedia tools — at the expense of math, reading and writing fundamentals. They say the technology advocates have it backward when they press to upgrade first and ask questions later.

how the district was innovating.

On Wednesday, Mr. Gardner will celebrate his 95th birthday with the publication of another book — his second book of essays and mathematical puzzles to be published just this year. With more than 70 books to his name, he is the world’s best-known recreational mathematician, and has probably introduced more people to the joys of math than anyone in history.

Standardized tests certainly aren’t going anywhere. States that have dumped exams aligned with the Common Core aren’t dumping high-stakes testing; they’re just switching to new tests, like the ACT’s Aspire. (Other ACT offerings include the Explore, the Engage and the Compass. Apparently standardized tests are titled by the same people who name midsize sedans.)

The Common Core is the way math was taught before. True, the new South Carolina standards are 92 percent aligned with the Common Core. But the Common Core was 97 percent aligned with the math standards South Carolina was using before! The term “number sentence,” which the comedian Stephen Colbert mocked, is 50 years old, and the kind of problem it describes appears in textbooks from the 1920s.