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What I have learned about the students I have taught throughout my career is that the trend begins with students as young as 8 or 9 who have already been turned off to mathematics and science. They have been taught from societal experiences, home events, and by our teachers, that the subjects of mathematics and science are about solving a large numbers of problems as quickly as possible or reading large passages from a textbook.

young students' natural inclination to want to learn more about mathematics and science in order to make sense of the world.

Our instruction must change to allow our students a fundamental understanding of important mathematics and science concepts and we must do this in ways that continue to keep our students excited about these naturally interesting subjects.

Research confirmed in the 1990s that students learn more by grappling with open-ended problems, like creating a computer game or designing an alternative energy system, than listening to lectures. While the National Science Foundation went on to finance pilot courses that employed interactive projects, when the money dried up, so did most of the courses.

he also says it’s inevitable that students will be lost. Some new students do not have a good feel for how deeply technical engineering is. Other bright students may have breezed through high school without developing disciplined habits. By contrast, students in China and India focus relentlessly on math and science from an early age.

The Massachusetts Institute of Technology has long given freshmen only “pass” or “no record” grades in the first half of the year while they get used to the workload.

the grades in the introductory math and science classes were among the lowest on campus. The chemistry department gave the lowest grades over all, averaging 2.78 out of 4, followed by mathematics at 2.90.

MATTHEW MONIZ bailed out of engineering at Notre Dame in the fall of his sophomore year. He had been the kind of recruit most engineering departments dream about. He had scored an 800 in math on the SAT and in the 700s in both reading and writing. He also had taken Calculus BC and five other Advanced Placement courses at a prep school in Washington, D.C., and had long planned to major in engineering. But as Mr. Moniz sat in his mechanics class in 2009, he realized he had already had enough. “I was trying to memorize equations, and engineering’s all about the application, which they really didn’t teach too well,” he says. “It was just like, ‘Do these practice problems, then you’re on your own.’ ” And as he looked ahead at the curriculum, he did not see much relief on the horizon. So Mr. Moniz, a 21-year-old who likes poetry and had enjoyed introductory psychology, switched to a double major in psychology and English, where the classes are “a lot more discussion based.”

Mr. Moniz’s experience illustrates how some of the best-prepared students find engineering education too narrow and lacking the passion of other fields. They also see easier ways to make money.

Mazzocco and her colleagues previously found that the ability to estimate approximate quantities without counting generally improves during childhood and is related to math achievement

Mazzocco’s group studied 71 ninth-graders whose math abilities had been tested annually since kindergarten. Students completed two quantity estimation tasks. In one series of trials, participants saw an array of blue and yellow dots flash for a fraction of a second on a computer screen and indicated whether more blue or yellow dots had appeared. In other trials, students saw nine to 15 yellow dots flash on a screen and estimated how many dots were shown.

Mazzocco’s group studied 71 ninth-graders whose math abilities had been tested annually since kindergarten. Students completed two quantity estimation tasks. In one series of trials, participants saw an array of blue and yellow dots flash for a fraction of a second on a computer screen and indicated whether more blue or yellow dots had appeared. In other trials, students saw nine to 15 yellow dots flash on a screen and estimated how many dots were shown.

Thirty-six percent of high school seniors in 11 states scored Below Basic in math on the 2009 National Assessment of Educational Progress, the nation's exam of student achievement

One out of every four eighth-graders in the entire country is mathematically illiterate.

the percentage of U.S. doctorates in engineering awarded to foreign students has increased from 47 percent to 57 percent between 1989 and 2009

Mr. DuBois wanted the system to become smarter in how it invested in people, talent, and technology, as well as do a better job of taking advantage of its size and resources.

One study by the college system found that only 16.4 percent of students sent to developmental-math classes ever managed to pass a college-level math course.

Recent high-school graduates are among the most vulnerable. They become frustrated when they learn they can't immediately enroll in credit-bearing classes, and they sometimes leave college even before taking a single course.

the court ruled that you can't patent mental processes—even if they are carried out by a computer program.

no-patenting-math rule doesn't apply if the math in question complicated enough that "as a practical matter, the use of a computer is required" to perform the calculations.

So you can't patent calculations that could be done with a pencil and paper. And such calculations remain unpatentable even if the steps are encoded in a machine-readable format. But this leads to an obvious question: why is software patentable at all? All software consists of sequences of calculations that could, in principle, be done with a pencil and paper.

Jobs in science, technology, engineering and mathematics are growing at four times the rate of other career sectors, says the partnership, and Iowa's economy increasingly relies on high-tech jobs.

Researchers at the National Institutes of Health have created a mathematical model -- and an accompanying online weight simulation tool -- of what happens when people of varying weights, diets and exercise habits try to change their weight.

However, the computer simulation of metabolism is meant as a research tool and not as a weight-loss guide for the public. The computer program can run simulations for changes in calories or exercise that would never be recommended for healthy weight loss. The researchers hope to use the knowledge gained from developing the model and from clinical trials in people to refine the tool for everyone.

"Mathematical modeling lets us make and test predictions about changes in weight and metabolism over time," Hall said. "We're developing research tools to accurately simulate physiological differences between people based on gender, age, height, and weight, as well as body fat and resting metabolic rate."

While most Waldorf schools are elementaries, the Bill & Melinda Gates Foundation helped launch the first public Waldorf high school four years ago at the George Washington Carver School of Arts and Science in Sacramento, Calif., replacing a failed America’s Choice program in the building. Test scores have since risen dramatically: In 2008, 67 percent of 11th-graders scored “far below basic” or “below basic” in English; in 2011, just 12 percent did. Teachers are happier as well, says principal Allegra Allesandri. While many teachers spent the summer boning up on content, Allesandri’s teachers also honed skills in bookbinding, painting, and felting. Many Carver faculty gatherings include singing in harmony and playing games. “Those skills, which might be about singing, are also about working together successfully,” she says.

For example, at the Woodland Star Charter School in Sonoma County, Calif., test scores for 2010 show a stunning 81 percent of the second-graders scoring “below basic” or “far below basic,” compared with 32 percent of district peers. By eighth grade, however, none of the school’s students score in that level (in fact 89 percent are “proficient” or “advanced”), while 19 percent of district peers score in the lowest two levels and just 56 percent in the top two levels. Results have been less dramatic at some Waldorf-inspired charters, whose students in upper grades have scored about the same as district peers.

They still do project-based activities, start class with a verse perhaps by Albert Einstein, and end by thanking the teacher. But Bishop says the texts and 40-minute daily math lessons “look more like public school.”