Finding Balance

Yesterday I was at school for nearly seven hours, an hour and a half of which I taught Geometry CP. I was teaching on Proving Isosceles Triangle Conjectures and, overall, it went very well. I was a lot more comfortable this time and the students all behaved very well. During the lesson, we somehow got into a discussion about different dimensions and planes. The students were all asking very good questions and it was a mathematically rich discussion. It did not really have anything to do with what we were talking about, but it is an interesting topic and most of the students were actively engaged in the discussion, trying to grasp the concepts. That diversion went on for probably about 20 minutes, and I did not get to finish my lesson as a result. To me, it was more important that the students were thinking mathematically and asking lots of questions that it was for us to steam through the topics that we were supposed to cover.

During lunch, I talked with my mentor teacher about the lesson. He told me that he thought it went very well and that he thought I handled things well. At one point, they asked me a question that I didn't know, so I told them that I didn't know. One of the students commented that he really appreciated my ability to admit that; my teacher later told me that he agreed. I was glad that went over well with the students. However, I know that students would not like it if a teacher said that every day, so it's something that I'd have to use sparingly. My teacher reminded me that with the Promethean Board, you can access the internet and said that would be a very useful resource in the future--something I'll have to keep in mind.

We also discussed how to balance between rich mathematical discussions and covering standards that must be met. Obviously this issue is important to me because I love when students ask questions stemming from topics covered in class that shows their curiosity and interest in math beyond what's being covered, but we still have to cover certain material. He asked me if the tangent we discussed addressed any of the standards covered in the lesson I taught and pointed out that if side topics build a stronger foundation of understanding, they are worth it. Otherwise, it will not be as beneficial to the students and they could use that to try to get the teacher sidetracked so that they never really have to do any work (kind of like in Mr. McCourt's classroom in his book). I know that students are smart about trying to get out of work, so I will have to work to see when that is the case. As a teacher, I will try to be open to talk about other topics to the extent that it will be helpful to the students. Otherwise, I need to limit those conversations to ensure that my students will know the material they need to know for End of Course exams and other tests.