From what I've learned so far, Developmental Learning theory is the most essential part of teaching something. No matter who your students are, you must have a plan to bring the students from the concrete to abstract.
In my sophomore year of high school, I had a geometry teacher named Mr. Bouris. For the most part, he was a very laid back guy and had a pretty good sense of humor. He occasionally liked to poke fun at individual students and would sometimes spray water out of the bottle that he used to clean his overhead projector with. He definitely was fun to be around and usually was pretty approachable. However he had no idea how to teach geometry.
When he did lessons, he would never put any actual effort into teaching us. He would just pull out the overhead projector and draw out the examples in the book. Instead of inviting students up to the board to maybe show a few problems and see if they could do it themselves or make concrete models that would make it all seem sensible, he would then just assume that we understood it all. Although some students understood everything after those few examples, most of us would be absolutely perplexed as to what was going on. Then he would give us a practice worksheet that we would turn in the next day. Usually I would just stare at the sheet and then go up to ask him for help. He would attempt to explain it again with the exact same example from the book, which would make me even more confused. When I would ask him if I come in later, he would tell me that the only time he could work with me was during the class.
Looking back, I wonder how on earth I passed that class. Although I admittedly have never been the best with math, he seemed to just make things worse. Throughout the majority of the class, I had a pretty good feeling he did not want to be there. He actually told us one day that he preferred teaching Algebra 2 over Geometry any day. Ever since I've had him as my teacher, I have made a solemn vow to myself that I will never teach like him.
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