The teachers solves 4 problems, during which time the students are reminded that the compound inequality means that both inequalities need to be satisfied (not in those words), how to graph solutions on the number line, various notation, and so forth. They arrive at problem numbered 4 that reads:
While working out the problem the teacher says: "Now listen very carefully. We have to pay attention to our signs". They arrive at the following:
and proceed to graph it:
Students make no comment, they copy down the solution and the class proceeds to the next problem. A conversation similar to this happens as the next problem is being solved:
Student: "So, if the bigger one is on the left then they go out, and if it's on the right then they go in?"
Teacher: "That's right"
After the class, I brought problem number 4 to the teacher's attention and got the following response:
Teacher: "I realized it as I was writing it down. I'll fix it by the fifth hour. I didn't want to confuse them."
I, dumbfounded: "?!"
How and when do we teach our teachers that making a mistake in front of the classroom happens, and is not something we should hide and sweep under the carpet. I remember making mistakes in classes I teach; we all do, sooner or later. I apologize every time I do as if I had wasted their time, and not taught them something of value. We make mistakes, but we need to deal with them in a responsible manner. Go back, fix them, show your students that even when you know something it is not shameful to make a mistake, but it is to hide it. Show your students that we are learning all the time. And that we should not think that we ever learned it all. I think I wrote about this before, but it seems that our teachers think that there is nothing more they need to learn once they have their teaching certificate. They are ready. Are we really?