I know I am showing my age here, but remember the old Arid deodorant ad, whose tag line was "Never let 'em see you sweat"? This is certainly good advertising for antiperspirant, but it is terrible advice for effective teaching.
When we first go into the classroom, we all want the kids to think we know everything. We want them to believe we are never wrong, never make a mistake, and never don't know the answer to a question. This is nothing but an ego trip, and the sooner you drop it, the more enjoyable your classroom experience will be. Of course you get answers wrong and make typos on tests. You are a person, not a programmable teaching robot.
This is about more, however, than just admitting you are human. There are pedagogical reasons for letting the kids see you make mistakes. They also get to see you fix them. If all we ever present to them is perfect pre-solved problems, they never see the thought process behind solving the problems. My weakest area in physics has always been electricity. I have such a tenuous grasp on voltage that it can be completely undone by a question. I have to review Kirchoff's Rules for circuits every year before I teach it. Last year, because of our seven stinkin' snow days, I forgot to review it. In the middle of the first example of a combination circuit, I realized I was doing it wrong. I had to stop and ask the kids to let me think for a minute. I talked through the problem out loud, reminded myself of the rules, undid what I did wrong, and confessed to the kids that this had always been difficult for me. This threw them for a minute, but I said, "Let's do another one, so you can actually see one worked correctly from beginning to end." I think it was important for them to see this thought process happening in front of them. When they went home to work similar problems, they probably got stuck along the way too. They won't feel dumb if they know that the teacher also gets stuck in the same spot.
This is not to say you should intentionally mess things up just so kids can see it. They know an act when they see one. This just means that when the inevitable happens, the way you react to it will have an impact on them. If you try to fake it, they will not respect that. If you get upset that you were wrong, you teach them to fear being wrong (which, in turn, teaches them not to learn anything new). If you take the time to solve the problem, you teach them to solve problems.
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