When I have TAed calculus courses and led discussions, while I did not find myself grossly inept at interacting with students, there was a bit to be desired with making discussion interactive. I am probably average or below average with interpersonal skills. My evaluations always came back with the lowest scores on engaging with the class--asking and answering questions. I have never had my students work in groups either. It takes a bit of social courage to involve the students. What are strategies for getting students actively involved in discussion?

When I have TAed calculus courses and led discussions, while I did not find myself grossly inept at interacting with students, there was a bit to be desired with making discussion interactive. I am probably average or below average with interpersonal skills. My evaluations always came back with the lowest scores on engaging with the class--asking and answering questions. I have never had my students work in groups either. It takes a bit of social courage to involve the students. What are strategies for getting students actively involved in discussion?

EDIT: With respect to some of the answers and comments, things that are not an issue include mastery of the material, preparation, good diction and clarity of words, and otherwise lecturing forms of communication. One-on-one tutoring or office hours with small groups I carry out successfully, though I am not too personal and mostly I just respond to questions with explanations or do certain problems they are interested in.

I have the impression that engagement is much better than simply lecturing. I am asking for an explanation of how engagement improves the quality of learning calculus and the specific steps and tasks I can take that I can learn as a skill, not as something that comes naturally.