Below is a list of ideas regarding the first day of section, generating class participation, running section, and preparing for section.

FIRST DAY (aside from obvious technical stuff):

Encourage students to talk to one another for a few minutes (exchange emails, get more comfortable with fellow students)

Tell jokes

Start taking roll before class evens tarts by just introducing yourself, getting them to say their name

Have them mention their major, favorite color, hobby and tell them you are doing this to help them identify possible study group members

Have them write down their schedule so as to pick convenient office hours or let them vote on a short list of possible hours -- this shows your sincerity in wanting to help them

Discuss how the class will be run, ask for feedback

Discuss and demonstrate how to read mathematics -- with pencil and paper ready to work out examples and think about theorems.

Discuss how to communicate questions via email

GENERATING CLASS PARTICIPATION:

Tell them you won't go on until someone answers your question

Take an opinion poll and ask why so many are abstaining :) This helps you assess the class too.

Be the scribe at the board and only write what they tell you to write

Repeat, clarify, or write down questions that no one is responding to -- wait a long time

Encourage students to correct your mistakes by telling them that that is a form of class participation -- thank them when they do

(ideas that were emailed to me by Melissa after the discussion):

Ask for examples (e.g. "Someone tell me they're favorite exponential function." "I need a subset of the real numbers that's not an interval.")

Have the students choose which example you do (e.g. "I'll do (a), (b), or (c) from problem 5, which one should I do?" This at the very least gets someone to say something; but since they only have to choose from a list, it's not asking much from them. This also gives the TA ammo against students who complain that he/she only does the "easy" problems in class.)

Have someone come up to the board (not just for working out a problem; e.g. ask a student to draw a graph, and you will then have the class work on finding what the integral of it is)

Have students work on a problem on their own (at their desks) before talking about it (of course, this only works for short problems), and wait until you have seen pencils moving and students actually working on it before talking about it (this is a way to get participation from students that are too shy to be singled out)

To keep one student from monopolizing the answer-giving (and, more importantly, keeping the other students from relying on that person to do the answering for them), say you'll wait to hear three answers/guesses/whatever. I especially like to use this when working on True/False and Yes/No questions. This is also nice to assess the class as a whole. Often you'll get split answers (two Ts and one F), but if you get all three the same, that can really tell you something about how the class is doing and what they're getting or not getting.

DURING SECTION:

Try to avoid doing entire problems for them unless you are providing them with a model of how you want to see them write

Lecture on the particular aspects of that weeks material that you think are the most confusing but encourage questions and use more examples than a typical lecture

Emphasize that you, the book, mathlab, CLAS are resources and that you look forward to seeing them in office hour -- maybe write office hours on the board each time -- this might be especially important to transfer students

Write out definitions repeatedly and use mathematical language carefully so they get used to doing the same

Demonstrate how the book can be useful in class so that they get in the habit of using it properly

Repeat your goals for the class or your guidelines two or three weeks into the class to remind them of where this is all going

PREPARING FOR SECTION:

To be efficient, avoid writing out the solutions to every homework problem but look over them and write out a few -- especially those that you might expect them to ask about

Outline the key concepts for yourself and think of questions that you can ask the class to get them thinking about these

Read through the book and look for statements that are vague or maybe even incorrect (especially in the answer key)