I visited a new classroom and a new teacher. Although there are great similarities between the two classroom, there are some major differences as well. One of the things that I liked immensely in the new classroom was teacher's constant inquiry and/or revelation of alternate methods for solving problems. The beginning of the class was spent by going through some problems from the homework. 4-5 students were on the board at the same time giving their solutions to the problems that other had asked to see. Once they were done writing, each student had to explain their solution to the whole class. Whether the solution was correct or needed fixing, the question that would be asked was whether somebody had a different solution. Sometimes there was, and they would go to the board and write it out. If nobody offered anything, the teacher gave her solution. I am pretty sure that on all but one (sample of 10) they have shown more than one strategy.
One of the things that bothers me and seem to be common across the board: each class was interrupted by something/somebody from the outside anywhere between one time and three times during the class. I am not talking here about student's random talking, but PA/phone/students walking in or out/student council announcements/teacher aids.... This is something I do not remember ever being done when I went to high school. I don't even know if we had AP!