One possible way for us to try to empathize our students is to open the possibility for them to speak, and expose their difficulties, their dreams, their yearnings, their desires, their fears, their strengths, and their weaknesses.
In a project developed with one of my classes, at the Publicity faculty, I requested that publicity and awareness campaigns be created on topics that here in Brazil are always difficult to address due to the high level of prejudice and discrimination.
The teams worked on these topics:
1 - Human rights
2 - African Religions
3 - Homosexuality
4 - Racism
5 - Drugs
At all times my students and I discussed all these topics openly. We had a group of homosexual men and women, some people adept at Candomblé, two blacks, people of evangelical religions, who in Brazil are usually conservative, anyway. We had a great setting for each person to talk about how he felt, tell his story, and so show that, although different, they were people, and they had a lot more in common than they seemed.
The results were wonderful. On the day of the advertising campaign presentations, each team talked about their theme and everything they learned about respecting people, and looking at the world empathically with each other's gaze
See if this can work for you.