"Such happiness as life is capable of comes from the full participation of all our powers in the endeavor to wrest from each changing situations of experience its own full and unique meaning."
- John Dewey
The interactive, in-class participation is more likely to occur with smaller classes (i.e., classes with less than 25 students) or in subjects where the material naturally lends itself to human interaction (e.g., performance-style courses). It becomes even more rare in courses that are steeped in the "lecturing professor" tradition (e.g., mathematics).
Despite these obstacles, active participation in college and university classrooms should be highly encouraged, both by your professor and by you. You need to take every opportunity to engage actively in the classroom to further your understanding of the subject matter. You should encourage your instructor to experiment with their course and to allow students to openly discuss ideas during class sessions. In any case, you should never feel embarrassed to ask questions in class. You should also answer as many questions from your peers as possible. It is surprising how much we learn when we teach someone else.
Outside of the classroom is truly where participation pays the most dividends. It is common for students to think of homework as a list of exercises they must get through before doing something else they enjoy; however, this approach to scholarly activities outside the classroom is detrimental to your education. Homework is your opportunity to engage with the material on a more personal and introspective level. For true understanding to occur, you must consciously participate in actively deciphering the concepts and ideas that are trying to be "exercised" in the homework. Moreover, while learning a subject, you should make every effort to keep the material at the forefront of your imagination to see if you can relate it to the world around you.
My Style: As far as participation in the classroom, I sincerely enjoy having students who participate intellectually and encourage discussion as often as possible. A classroom where my voice is the only sound is boring to both you and me.
I know from experience that a university degree worth receiving can only be obtained by complete immersion into a subject. As such, I also try my best to get students to think about mathematics outside the classroom. I commonly assign homework that requires a deeper level of thought and processing than just computations. Additionally, I have been known to assign projects. These projects often require perseverance and a dedication to truly understanding the material.