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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.

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.

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.

Back-to-school facts: $7 billion-plus in shopping and everything else

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.

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.”