This is a topic I just discussed with my mentor teacher at Miramar on Friday. My relationships with students have changed drastically from when I began tutoring in high school and college and I didn't recognize it until quite recently. This requires a bit of background to fully understand.
When I started tutoring, it was to my peers in high school and college. We were the same age and more or less knew each other, at least as acquaintances, if not friends. I also had much longer hair that was poofy and frizzy and weighed about 155 pounds with no facial hair. Now, I mainly tutor people of different ages, who are not acquaintances or friends to begin with, and my physical appearance has changed as well. I keep my hair short (often buzzed), weigh 195 pounds, and usually am not clean shaven. I have also gone from the "B" student and class clown, to an "A" student and quite serious most of the time.
Basically, what this all comes down to is that over the past few years I have gone from being rather boyish and unintimidating to somehow intimidating to many of my students, whether because of physical looks, education level, or seriousness upon getting to work. I have been told this fact by several of my own classmates in the masters program and have noticed it since being made aware within the classroom as well.
Since figuring this out over the last few months, I have made a really big effort to be more approachable. I try my best to be as open and unintimidating as possible and this has been done mostly through attempting personal connections. Rather than launch straight into work (which I view as efficient and the best use of the student's time), I take as much as time as needed for the student to open up and get talking. This can take two minutes ("How was your weekend?") or almost the entire class period.
In the past, I would have seen using so much valuable time talking about personal matters and ignoring the work as a waste, but now I realize that it absolutely is NOT. Even if we don't get to the "real" work today, we will be able to get through much more work in the coming weeks and months. This initial upfront "cost" is actually an "investment" that pays off big down the road. I also don't feel so guilty about letting students get "off task" now, since I know this is just the normal part of getting to know one another. Without taking this time in the beginning, I often spend months without connecting to students and really being able to help them, which turns out to be a much bigger waste of both our times.
In my case, not connecting can often mean students won't learn from me. That is what rapport comes down to. You can be the best teacher in the world (not saying I am), but if students don't like you, respect you, or aren't interested in you, they won't listen. If they don't listen, it becomes really hard to learn.