This week, Gmerek's students have been working on combining all the rules they've learned this year to synthesize complex derivatives. For the most part, I've been individually explaining the ins and outs to them, as well as going over commonly overlooked trivialities. I'm pretty sure that the students are making great progress, but I definitely had trouble this week as they began to head in to methods and rules I hadn't used in a while. My memory was fuzzy, but I was able to still explain things without confusing the students. I tend to make the students explain the problem back to me or tell my why my method works to ensure they understand. As the topics get more and more complex, I find myself having to try two or three methods to explain things to the students, so I'm seeing the advantage of really knowing your topic well before you explain it. This also helps in being able to explain WHY a student was wrong. They often look at their work and understand what the key says, but they don't see why their work got the wrong answer. Being able to not just point out mistakes but EXPLAIN why they're wrong makes students much less likely to repeat them. In general, I'm continuing to learn valuable lessons each week through my observations, despite staying in the same place. From talking to Gmerek and Horne, it sounds like they continue to learn new tricks everyday too, even after years of teaching the same class. I look forward to that as I become a teacher.
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