Perfection is the enemy of good. When I first got into teaching, an instructor I admired told me "If you're going to teach for thirty years, then teach for thirty years. Don't teach one year thirty times." I am always adjusting my teaching based on new things that I've learned, new approaches that students have shared and the needs of the particular group that I have. What worked great the last three classes may fall flat the fourth time.
I am no stranger to making a math error on the board during a class. If I catch it first, then I invite the students to spot my error. Once they do, we discuss how it can be corrected and what kind of an effect the error would have on the final incorrect answer. If the students catch me, I have them explain why what I did was a mistake. Was it a 2+2=5 arithmetic error? Was it a dropped negative sign? Was it an illegal algebra maneuver? Mistakes are an inevitable part of learning mathematics and I like to be living proof that no matter how long you've practiced or how many years you've taught, no one is immune to making mistakes.
