Before asking this question, we should examine the definition of compassion. According to Wikipedia, "The English noun compassion, meaning to suffer together with, comes from the Latin."
Can students be taught how to suffer with others? In my opinion, the answer is yes but the lessons will not be learned in a classroom.
My dad was a church minister and visited numerous people in hospitals and nursing homes. Sometimes I accompanied my dad on these visits and I also watched him comfort grieving people at funeral homes. My dad was a compassionate role model.
Open Colleges produced this infographic asking, "Can we teach compassion?" The infographic examines the subject of community service performed by college students and reports that "38% of student volunteers are introduced to volunteering through their university or students' union."