Teachers and other public education employees, such as community-college faculty, school psychologists and janitors, are quitting their jobs at the fastest rate on record, government data shows.

A tight labor market with historically low unemployment has encouraged Americans in a variety of occupations to quit their jobs at elevated rates, with the expectation they can find something better. But quitting among public educators stands out because the field is one where stability is viewed as a key perk and longevity often rewarded....