Math - Calculus
Time Tutored: 10:15-11:30am
Additional Billable Time: NA
Previous Quiz/Test Scores: 20/28
Next Scheduled Session: Sometime next week
First, we looked at S’s test on critical points, maxima and minima, etc. Her score on it was not very good, but I feel that this score does not reflect her knowledge of the material. The test, as the teacher himself admitted, was simply too long to be finished in an hour. All of S’s mistakes didn’t have to do with her understanding of the material, but rather were careless mistakes incurred by rushing to finish the test.
We moved on from there and discussed optimization problems. We talked about the standard 3-step process to do these, and worked a few examples. Then, we discussed related rates, a type of problem very similar to optimization, and worked a few examples. S really had no difficulties with the techniques used to solve related rates and optimization.
At this point, I decided to build on S’s knowledge of implicit differentiation, and taught her about two applications of it: logarithmic differentiation and inverse function differentiation. We discussed the theory of these two methods for arbitrary function, the situations in which these methods apply, and worked a few examples for each. We used these techniques to prove some differentiation formulas that S knew but didn’t know why they worked, such as d/dx(ln(x)) = 1/x.
Today’s lesson with S was very productive, as we covered the material she’s studying now and even went past it by discussing some new concepts. We talked over what went wrong with her test last Monday, and came to the conclusion that it was more the teacher’s fault for giving them such a long test than S’s fault, because she does know the material. Please see the tutoring recap below, and don’t hesitate to contact me if you or S have any questions.
Up to today, I’ve been doing most of the talking. However, I think that for S to master the material, it would be better if I let her do more problems herself. Thus in the future, I’ll explain the material and work an example or two, but also let S work a problem to make sure she understands the material fully.
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