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Moving toward that goal, a more comprehensive mathematical model of human metabolism was used recently to design an NIH clinical trial that is comparing the effects of reducing fats versus carbohydrates in obese adults.

Institutions are equally affected. A recent report by the Community College Research Center put the annual cost of remediation at $1.9-billion to $2.3-billion at community colleges and $500-million more at four-year colleges.

There is growing recognition that the traditional semester-long course sequence used by many community colleges doesn't work, says Michael Lawrence Collins, associate vice president for postsecondary state policy at Jobs for the Future, a Boston-based nonprofit that studies education and work-force issues. It's inefficient to have students take up to a year and a half in remediation when many need just pieces of what they're being taught.

The Virginia system is betting on that promise. Its colleges will soon replace their semester-long developmental-math courses with nine units, which can be taken as one-credit classes or Web-based lessons with variable credit hours that allow students to complete more than one unit in a self-paced computer lab and classroom. The number of units that students are required to complete will depend on their placement-test scores and intended program of study. Students focused on the liberal arts will have to show competence in only five units, for example, mastering basic algebra concepts such as linear equations. Students who plan to pursue careers in science, technology, engineering, math, or business administration must complete all nine units.

Although he has help from a tutor in the class, it's a lot to juggle, he says. Mr. Wyrick does like how the Web-based class allows him to peek at students' quizzes in real time and track their progress a lot faster than by sorting through homework and test papers himself. "It allows me to intervene even before they ask for help," he says.

There is one certainty. The Virginia Community College system is not the only one anticipating the outcome. Equally curious are researchers and other colleges searching for successful ideas. "There is a risk," Mr. Collins says, "but there is also power in being that bold."

The Virginia Community College system is poised to find out. Starting in 2012, it will adopt a new systemwide developmental-math curriculum that will allow students to focus only on those math concepts they haven't already mastered rather than taking a series of semester-long math courses.

Half of all incoming students in the system need developmental education—and three-fourths of those students fail to graduate or transfer within four years.

Working with the Dana Center, the community college association was able to get all 50 two-year college presidents to sign on.

The Texas project is inspired by the Carnegie Foundation’s work, developed with the Charles A. Dana Center at the University of Texas at Austin, in which students needing math remediation weren’t all put on a path toward calculus.

Kay McClenney is a University of Texas at Austin project director who helped develop a recent report showing the scope of the remediation problem at the state’s community colleges.

Charles Cook, vice chancellor for instruction at Houston Community College. “I think the Statway project really has it right, where we’re looking at mathematical reasoning and problem solving and how math can serve you as a tool to further understanding, further investigation and further knowledge.”

Carnegie’s $14 million Quantway/Statway initiative is developing two mathematics programs: one-year courses that build quantitative literacy (Quantway) and statistical proficiency (Statway). They’re infusing both with teaching strategies that build students’ confidence as math learners.

Theoretically, you could have performed the calculations with a pencil and paper, but no one actually did so. Yet the Supreme Court still held them to be unpatentable mental processes.

The Federal Circuit displays a similar confusion about a more recent case, this one involving an algorithm for digital image half-toning. The court upheld the patent despite the fact that mathematical formulas were "admittedly a significant part" of the patent's claims. In Tuesday's opinion, the court argued that the half-toning patent was different from the fraud-detection patent because the half-toning algorithm "required the manipulation of computer data structures (e.g. the pixels of a digital image and a two-dimensional array known as a mask)."

Of course, a "computer data structure" is just a way of organizing numbers and symbols. When I served as a teacher's assistant (TA) for computer science courses in grad school, I would regularly draw diagrams of data structures on the whiteboard and perform example calculations on them. Similarly, many branches of math involve manipulating "data structures" like ordered pairs and matrices—presumably the Federal Circuit doesn't think you can patent new results in linear algebra because "data structures" are involved.

At the time, the technology we used (in math class) was a graphing calculator,” he said. “Today, these kids have the privilege to learn math in a new, innovative way

Only the Fuse algebra application and a few key tools are loaded onto the devices. At school, students are blocked from inappropriate sites via firewalls. The App Store, where iPad users can purchase games and other applications, is locked on the device, but school officials are looking at opening the online store in the future. Freshman Catherine Rodriguez, 14, flashed a big smile as she received her new iPad. Math isn’t her strongest subject; she hopes the new technology will help her, she said. Passing math is a big concern for Rodriguez’s mother, who took three years to pass pre-algebra, she said.