All students deserve a little bit of respect, especially from their teachers. If these students are AP or Honors students, then they definitely do not need to feel patronized, especially on the first day.
Many teachers use the first day to go over the syllabus, which can create a stagnant environment, and worse, a lost teaching day. In all of my classes, I start teaching a full blown lesson on the first day. My goal with this approach is two fold.
1) Set the pace that the material will be covered at instantly
2) Show the students that I think enough of them to understand that they can read.
Below is how my first day of AP Calculus AB is structured. Keep in mind, that I am teaching in a 45 minute time period.
1) Hand out syllabus and review the honor code (required at the school I teach) roughly 5 minutes
2) Numerical approximation of limits (tables generated by hand and via calculator) 40 minutes
The numerical approximation of limits is done via a student activity, which is concluded with a class generated definition of a limit. In this process, I have also set the expectation of where all numerical answers must be rounded (3 decimal places for AP) and given a rough review of basic algebra skills.
Normally, the students are excited at the end of this class, though they are not happy with the homework assignment (generally 5 questions... I mean really, why complain). The next day they have a short quiz to start class (error analysis with a justification) and we move forward to graphical determination of limits. All and all, a quick start to a new year.
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