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50% scored proficient or better in math, compared with 48% last year. The scores are the highest since the standards-based testing began in 2003.

Students who were considered at grade level — or proficient — in English-language arts increased from 41% to 44%. In math, from 39% to 43%.

Over the last four years, the total of Reseda students who score at grade level or better in English rose from 39% to 47%; the percentage actually dipped slightly this year. In math over that period, the figure rose from 18% to 22%.

I suspect that testing spatial reasoning, especially in a standardized way, is more difficult than standardizing the testing of math and verbal skills. Again, this has to do with the limitation of resources and the limitation of trying to test 3-dimensional reasoning on a 2-dimensional surface.

Which means that such skills are either seen as being “beneath” or unattainably advanced to most people.

Until that cultural change happens, though, I suspect that those kids and their parents interested in the world of spatial intelligence will still have to find avenues outside of school to hone their skills

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.

The report shows huge disparities among the standards states set when their tests are converted to the NAEP's 500-point scale. In eighth-grade reading, for example, there is a 60-point difference between Texas, which has the lowest passing bar, and Missouri, which has the highest, according to the data. In eighth-grade math, there is a 71-point spread between the low, Tennessee, and the high, Massachusetts.

South Carolina was the only state to drop standards on every math and reading exam during the study period.

The $49 Fuse application allows users to learn at their own pace, Blumenfeld said. If students miss a class, they can tap into about 400 video tutorials led by textbook author Edward Burger, a math professor at Williams College in Massachusetts. “Videos allow for anywhere, anytime instruction,” Blumenfeld said. “For students who might have missed class or didn’t understand the lesson, you can push a button and have it explained again and again. You have a teacher available anytime, anywhere.”

Test scores in Riverside, Calif., jumped 30 percentage points, from 60 percent to 90 percent proficiency in math, he said. A smaller iPad program in some of Chicago’s elementary schools also resulted in improvement, Ebert said.

Indeed, Algebra 1 is one of the most-failed courses in the School District, Ebert said. All Nevada 10th graders are tested on the freshman-level math subject before they can graduate. Only half of the students in Clark County passed the math section of the High School Proficiency Exam on their first try last year. A quarter of students won’t pass the math section by their senior year and, as a result, will fail to graduate. This year, the district has identified about 9,000 seniors who haven’t passed the proficiency exam. They are at risk of dropping out, Ebert said.

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.

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.”

And just because there’s a lot to choose from doesn’t mean all the programs possess the same ability to teach math on a long-lasting, conceptual level.

Although kids are quick to pick [technology] up, they’re not that quick at learning to relate it to a mathematical concept.

what you want is for students to realize, ‘I don’t need to memorize a thousand different rules. I’m beginning to observe commonalities.

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.

"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."

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.

"We still don't have an accurate way to determine who's dropping out," he said, citing studies that estimate L.A. Unified's four-year high school dropout rate at more than 50%. (The state-calculated dropout rate for L.A. Unified is 26.1%.)

The graduation rate is 68% for Latinos, 59% for African American students and 56% for students who are learning English. This compares with 83.4% for whites and 89.4% for Asians.

Overall, 74.4% of California high school students graduated in four years, according to state data; 18.2% dropped out. The remainder were still in school (6.6%), were in non-diploma programs for disabled students (0.5%) or left high school by taking the General Educational Development (GED) Test (0.4%).

This month, more than half of community college freshmen and at least a third of university students started college already behind. They're in at least one remedial course that does not count toward a degree, thus beginning at least four months—and sometimes years—delayed in getting the degree they enrolled to earn.

Like many of their fellow freshmen nationally, a whopping 95 percent of high school graduates from West Hills who received As and Bs in their senior English courses did not "pass" the placement test. Yet when allowed to enroll in college-level courses instead of remedial classes, 86 percent successfully completed college-level English, lost no time in their progress, and stayed on course toward earning a degree.

Only 24 percent of students placed in the lowest level of English remedial courses in California ever get through.