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An estimated 18.7 percent of high school students who enrolled in Utah colleges and universities needed remediation in 2007, said Holly Braithwaite, spokeswoman for the Utah System of Higher Education.

that would allow colleges to bill school districts and charter schools for the cost of remediating their students when they get to college. Dougall said it’s about making sure a high school diploma means something.

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.