I have TAed several content courses for graduate students in mathematics education. In this respect, my interactions with students may differ from the scenarios faced by others who have served as Teaching Assistants, e.g., for undergraduate mathematics students/majors taking Calculus.
(The courses I have TAed: Abstract Algebra, Problem Posing, Problem Solving, Proof Writing, Real Analysis, Set Theory, Topology; I've also TAed a separate Proof Writing course for undergraduate mathematics education majors, and an Intro to Calculus course for undergraduate [mostly] math majors.)
Some of the techniques I have used include:
Begin the semester by distributing an information sheet about office hours;
Set up a discussion board (through Moodle) so that students can ask questions and discuss them with one another;
Type up notes corresponding to what is covered in office hours - many students in education are also full-time teachers, so it can be especially tough for them to make the hours;
Encourage students to email me with questions - as long as they include their own thinking along with whatever they are asking - and tell them that if they organize study sessions somewhere on campus, then they should feel free to let me know (but that I cannot guarantee I will be available to drop by).
With regard to 1, I will paste below a template of the letter that goes out to every student on the first and/or second class meeting. With regard to 2, I usually give students a chance to answer each other's questions first; if a question has stagnated for more than a day or two, then I will address it. With regard to 3, I will link to two examples from an Abstract Algebra course I TAed: generally, I go through the assigned problems one by one, but often I will get them to modify the questions (e.g., what if we replace "cyclic" with "abelian"?) or to provide alternative proofs; sometimes I will turns comments into theorems. Finally, with regard to 4, I have noticed that asking a student to include his or her reasoning along with the questions can vastly decrease the volume of emails, and give both the student and you an insight into where the difficulty lies.
Example CA (course assistant) notes: Intro to Group Theory and Intro to Ring Theory
To the esteemed students of [course name] --
I will be available as a TA for your class starting [date/time] at [location].
Here are some things I am happy to do:
-address lingering confusion from material covered in class
-discuss problems from the book: old, new, complex, basic
-review past exams, help prepare for future exams, create sample exam questions
-brainstorm about incorporating topics from [course name] into a class you teach or might teach
-play Scrabble, if you bring a board and no one else is around
Here is one thing I will not do:
-discuss anything you haven’t already given some thought to
My email address is [ ].
If you are planning on coming in, it would be best to email me first with what you want to talk about. If you haven’t emailed me but get a sudden urge to drop by, that’s okay too.
Official Hours/Location: [ ]
If no one has appeared within 15 minutes or emailed me to say they’ll come in later, then I will leave.
If other commitments preclude you from coming in at this time, then please email me to reschedule.