I'm a teacher. This is one of the interesting decisions that goes into preparing lessons well. You want to plan well enough that you know what you are going to present, but not so well that it's all rote. Leaving room for yourself to make mistakes in front of students is really good.
I tell my students as often as I can, "Professional mathematicians, scientists, and programmers make mistakes all day, every day. They have just trained themselves to expect mistakes, and know how to deal with them when they arise."
I also tell students that if they are not making mistakes most days, they are not doing interesting or challenging enough work.
Some of the best profs I've had made mistakes deliberately. Making mistakes allowed them to point out common pitfalls and engage students by challenging them to find their mistakes.
Except it is absolutely infuriating for anyone trying to keep up with the lecture
I personally find whole "taking notes" riddiculous - I can't listen to the lecture because I'm constantly fighting to scribble down all the stuff that is being put down on the chalkboard
And then the lecturer makes a mistake and starts messing with stuff I already wrote down - final result is one horrible tangle of unreadable mess
I'm a teacher. This is one of the interesting decisions that goes into preparing lessons well. You want to plan well enough that you know what you are going to present, but not so well that it's all rote. Leaving room for yourself to make mistakes in front of students is really good.
I tell my students as often as I can, "Professional mathematicians, scientists, and programmers make mistakes all day, every day. They have just trained themselves to expect mistakes, and know how to deal with them when they arise."
I also tell students that if they are not making mistakes most days, they are not doing interesting or challenging enough work.