In his camp are those who say students need to concentrate on basics like math, literacy and history to prepare for college and the jobs of the future, rather than learning a narrow technical craft. In this view, bright students like Mr. Kelly, who have the potential to do college-level work, should be put on that path, or schools will have failed them.

What’s more, those in favor of academic reform worry that minority and low-income students will be automatically channeled into vocational courses. A rigorous academic curriculum, they say, is the best way to help all workers remain flexible, climb career ladders and prepare for a wider spectrum of jobs.

Recognizing that employment and income have expanded for those with college degrees, the president has said he wants America to produce the highest proportion of college graduates in the world by 2020.

Last year, fewer than a third of all 25- to 29-year-olds in the United States had earned a bachelor’s degree or higher. Advocates say the most compelling case for vocational education is that it keeps students interested in school at all. According to data from the Department of Education, about 75 percent of students who start public high school graduate within four or five years. But more than 90 percent of those who concentrate in career-oriented courses, a definition that varies by state, do so, according to statistics compiled by the Office of Vocational and Adult Education. (Eventually, after more years of school or passing a General Educational Development test, about 87 percent of all students complete high school.)

Strong vocational programs that start in high school, advocates say, can help students make the leap to one- or two-year credentials that are increasingly the ticket out of low-skilled, lower-paying jobs. In fact, 27 percent of people who get a vocational license or certificate after high school, whether at a community college or a profit-making institution, earn more than the average for those with a bachelor’s degree, according to the Center on Education and the Workforce at Georgetown University.

Career and technical education “can prepare you for jobs in which you’re going to earn a very solid middle-class income,” said William C. Symonds, director of the Pathways to Prosperity Project at the Harvard Graduate School of Education. “That’s not to say that you’re going to be a hedge fund manager making millions a year, but you will prepare for jobs that will pay more than a living wage.”