Great prompt, April! We liked thinking about this topic so much we wrote a whole book about it! Each chapter is focused on a different course (or major topic, in the case of Calculus.) We present lots of examples of student thinking, most drawn directly from the research literature. That's followed by a "What You Can Do" section, which presents research-based instructional strategies for overcoming the common teaching pitfalls.
What Could They Possibly Be Thinking?!? Understanding your college math studentsIf you're an MAA member, you can download a free copy. Login to the MAA site and go here.