It was nice to get back in to things after two weeks off! I spent 3 days observing this week, 3 periods each, so I think I really got in to a sort of groove. The topic was the same all three days; it's just complex application of a couple concepts (related rates and implicit differentiation) the students learned before Winter Break. The students are seeing just how many ways the tricks can be used to solve different problems, and the reason I love this topic is because it actually has a ton of real-world applications in everyday life, not just for obscure calculations. Each period responded to the work differently, but each day the students became more and more comfortable with the subject. I spent a lot of time drawing pictures and actually backpedaling to Geometry to explain old formulas the students needed to start their work. I think it's important to really make sure students understand the old stuff before they jump in to the bigger concepts, or else they'll forget something small later on. Most details just aren't significant when a student uses rote memorization, so I made sure the students understood where their volume, distance and surface area formulas were coming from, as well as connected the formulas from various shapes to strengthen their understanding with some general guidelines. Overall, they were very receptive and I think the students learned a lot this week. I know I did.
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