Good and bad teachers

 One of my high school teachers was very good. He taught the entire syllabus well, and gave us plenty of opportunities to think for ourselves as we solved problems. He got us to work through problems in groups of two on the whiteboards quite often, and he varied class activities quite frequently. He was very competent in his understanding of mathematics, and I felt well equiped for my subsequent studies after the training he provided. As I look to become an effective teacher, I can deploy his wide variety of class activities that kept us students on our mathematical feet.

One of my professors was a very poor teacher. He had a surface level understanding of the applied mathematics that he taught, and he specifically lacked an understanding of the pure mathematics that underlaid the constructs that he used. On more than one occasion, when we asked him probing questions, it became clear to us that he hadn't mastered the material that he was teaching. It seemed like he was simply guessing answers to our questions, and we saw right through this. In order to avoid his error, it is important first and foremost that I plan my lessons well and think about a variety of questions that I could be asked. I will need to demonstrate competence in every topic that I teach. It is inevitable that I will receive questions that I haven't heard the answer to before, so I must be honest about my ignorance.