I've taught before, both in the live classroom and online and I agree that students can tell. Even online they can tell, just with a mike and no video. I teach Algebra, and I know it cold from working with it for 39 years as an engineer and programmer. So its easy to spot trouble areas and help the students.
BUT, I am quick to point out to students that I make mistakes. As I lecture and solve problems, its easy to miss something. I love it when a student finds it first and tells me. It is a tension reliever when I laugh and say that is worth an attaboy or attagirl, and I tell them I like it when a student can catch me in an error. If I find the error first, I use it as an opportunity to explain that making mistakes is not really a problem, its finding them, checking your work to find them, and then correcting them. I ask why someone else didn't spot it before I did! I make it a challenge for students to find an error in my work. Sometimes I make a small mistake on purpose, like use the wrong sign just to see what they will do. After the first time, the students love to look for my errors. Its like a game. They catch on real quick that the end result is what counts not little correctable mistakes along the way. This also makes them cognizant of how to find their own errors as they solve problems. It makes them realize how important and useful it is to take the time to check their work. It develops a rationale in them for doing it right and knowing how to do that. It helps them way beyond learning Algebra, it helps them in any type of problem solving.
Sometimes I think that the professor who acts like he/she is perfect does not teach the best. To do what I do, you have to be confident in your knowledge of the subject and willing to laugh and poke fun at yourself. This is loving your subject and is what makes teaching - and learning - fun for all.
