“If you put an instructor to sleep 300 years ago and woke him up in a classroom today, he’ll say, ‘Oh, I know exactly where I am,” says Daphne Koller, co-founder of the online-education company Coursera. The same couldn’t be said for agriculture, manufacturing and health care, she notes.

The former professor of artificial intelligence at Stanford hopes to change that with Coursera, a platform on which universities such as Princeton, Yale and Stanford share some 1,000 courses free of charge. Later this year, the site, which...