You're thinking, "not my house." Yes, your house, your 1750 square feet (or 2500 square feet) of living space, cluttered garage and all. You don't even have to dust. They would love it. Here's why.
A home is a relaxed environment.
Even if it's not their home, students have a sense of home when they visit yours. They feel the freedom to be themselves. If they are away at school, your home can be a warm reminder of the one they are missing. This is especially true for internationals who often are away from home the entire school year. The invitation to a welcoming home and family environment can help them deal with homesickness and loneliness. If possible, you may want to offer some times that your homw would be open for students to come over just to study or do laundry.
Inviting students to your home helps them to know who you are.
Sure they get to hear you teach , but in your home they get the "behind the scenes" look into who you really are, flaws and all. You become more real to them when they know that you deal with the same every day life they do. And sometimes, things you never would have thought valuable to share become apparent in your home environment.
Inviting students into your home is an opportunity to model family life.
It's not a given that students today have grown up in a loving Christian home, and even if they have, seeing another family live out their faith together can be invaluable in a student's life. Invite a student or two for a meal with your family. Let them be a "part of the family" for the evening or a afternoon. Just be yourselves. Students will notice how you interact with and care for one another.
Paul says in 1 Thessalonians 2:8, "Because we loved you so much, we were delighted to share with you not only the gospel of God but our lives as well." Your willingness to open your home and let students into your life does not go unnoticed. It sends the message to them that you are not merely concerned with a lesson, or the college ministry in general, but that you truly do love them.