The students in Calculus were learning how to relate values of functions to their derivatives, and the derivativesof their derivatives (acceleration), so it was a really rough week for some of them. These concepts are mostly based in one's ability to visualize graphs and interpret data in their head, and calls for complete mastery of previous derivative information. The students can get easily confused by the difference between a decreasing slope and anegative slope. As it's also easy to mix things up as the person explaining the material, I have to be very careful with my wording, and do my best to help paint the picture the students need. It's almost impossible to explain complex calculus without drawing the graphs themselves (though technically this is simple in comparison to what they will do later), so I've been doing a lot of board work and arm waving. Though it's difficult sometimes to really get the right point across, it's extremely satisfying when the students truly understand because it's more obvious in these cases that the visuals were the key. This was yet another good week for practicing explaining complex concepts to students in unambiguous ways, and it's helping me expand my repertoire of strategies for getting the student to finish my thought for me. That's often the best way to know they got it.
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