Education Secretary Betsy DeVos and the head of a national teachers union sought to find common ground as they toured public schools in Ohio, but differences remained.

The school visit came just months after American Federation of Teachers President Randi Weingarten fiercely opposed the nomination of DeVos, a longtime advocate of charter and private schools. In the past Weingarten has accused DeVos of feeling "antipathy for public schools."

During the visit to schools in Van Wert, a town in northwestern Ohio, Weingarten said the two women have earned a reputation of "combatants" but that findi...