My approach to teaching philosophy is to convey the creative, practical, as well as rigorous side of philosophy. This involves breaking down prejudices, giving creative assignments, and showing how philosophical method can gain clarity on hard problems.
More than teaching philosophy, I teach students. Each student brings their own life experiences to the classroom and has their own goals. I make sure to keep an open classroom where students feel comfortable expressing themselves.
I like to start the first day of class with the pair of sentences on the board: Everyone is entitled to their own opinion. Philosophy is just a matter of opinion. Students typically believe each sentence is true even though they are in tension with one another. The philosophical discussion that follows helps to break down prejudices about what philosophy is and its usefulness. The main lesson we draw from the discussion is the distinction between the political freedom to say or believe whatever one wishes and holding epistemically justified beliefs that are truth tracking. It is the goal of philosophical method to root out unjustified beliefs.