What Makes a Good Math Teacher

So I am currently taking a physics class with some students who either recently graduated from high school or are in their senior year. I picked their brains a bit yesterday about what they thought made a good math teacher and what makes learning more interesting. One of them was all about the independent study route for those who understood the mathematics. He says he feels hindered by the class by having to wait for his classmates to catch up. In the meantime he is bored and frustrated. Another student commented that relating the mathematics to real life made it a lot more interesting. Hands-on activities also made learning more fun. I also learned, to my surprise that group work was not desired. The students said that group projects always ended up with one or two people carrying the work for the entire group. That hardly seems fair. I feel that group work is essential in students' learning. Does anyone have any ideas how group projects could be a fair learning experience?