It is particularly fun in physics to have students find out that if they do not understand the concept they had better pray they do not make any errors in the math. I was once stuck teaching (functionally substituting for the actual physics teacher who had to do an AP class during that period) a gifted physics class. The small crew of students who actually wanted to be there sat up front and after I and the physics teacher explained the situation to them thought it would be fun to mess with me in minor ways - up until the day that the brightest of them showed me a problem and asked me if his answer was correct. I looked at the paper and said "Nope!!" his mouth dropped slightly and he said, "Yes it is, you don't even know how to do the calculation!" "Quite correct", I said, "but I do know that if the forces are North and west, the boat is not going to go South and east! I am going to take a wild guess that you entered a negative in there somewhere accidentally!" Things went much smoother after that - but, then, they WERE there to learn.
LOL that must have been fun. It's wonderful when you get engaged enthusiastic learners.
Where too many teachers get confused is they expect the kid to walk in the door eager to learn all about their topic. Then also then pull out the "go to" lesson plans that they have used for years and expect the kids to listen with open ears and excitement.
But if you don't engage schema in the first place, then you have no idea who you are teaching. And if you don't know who you are teaching then you don't know what you are teaching. To me that's the key.
Last year I was asked to speak at a seminar for teachers with 5 other presenters. They asked me to go first and I gave an outline of what I was going to present. The coordinator was really freaked out when she asked me for a copy of my "speech" or presentation. I told her I couldn't possibly have one until I had met the audience and she was floored.
Then we all started and I spent about 10 minutes going around the room finding out about the audience members, why they were there, what they had learned, where they worked, what they taught etc e. Even if they had kids etc. Where they went to college.
I then taught for 45 minutes to a rapt interested audience. When the other speakers got up, two of them basically got up and said "well you know all this" etc etc because they came in with a set presentation and didn't have the ability to change it for the group.
During those two presentations, the cell phones came out, distracted bored audience members were bored after the first ten minutes because it was a set speech with a Power Point presentation that had absolutely nothing to do with them.
The other two speakers had time to adjust their presentation and one actually got up and said "Well I was going to present this but you know it anyway so lets move on to something else."
He was pretty good. At the end of the even the coordinator was told that most people felt the rest of the presentation was a waste of their time. Half of the people had left early anyway so they cut it short.
So key, you don't know what you are teaching until you know who you are teaching.
I'm sharing this example, but I learned the hard way. I too had several bad "lectures" where the audience basically was not interested in what I was teaching. They took notes etc, but it wasn't successful.
I doubt very many Math or Physics teachers here, ask their students why they are taking the class, what they know already, why they are interested and how it can relate to their real life. They just assume that the class will scramble to keep up because they want a good grade or a passing grade.