In what has been called the most competitive year ever for college admissions, Chelsea Link defied the odds to get accepted into Yale. Then Harvard.

Then came the fat envelopes from Princeton, Columbia, University of Chicago, Stanford and Northwestern University.

Making that feat still more extraordinary, Link has been home-schooled since age 5.

“I was a little nervous,” the Evanston 18-year-old said. “I was worried that I might not get into even one school.”

This isn’t false modesty on Link’s part, but an acknowledgment that many stereotypes about home schooling—think barn raisings and “Little House on the Prairie” wardrobes—are still entrenched.

True, she had nailed perfect scores on the SAT and ACT, is the reigning world Irish harp champion, aced all her AP exams and enjoys nothing more than kicking back with the latest copy of Scientific American…