Recent Tutoring Session Reviews
"Today we practiced with the properties of natural logarithmic functions. This included the power, quotient, and product properties. We practiced this first before we moved on to the derivatives of natural log. I reminded her of the importance of continuing to practice and memorize all of the derivatives she has learned so far. Towards the latter half of the session, I helped prepare her for the quiz on Friday which includes naming the specific derivative rule to solve certain equations. She was able to complete most of these problems with little help. We were able to complete her homework and go over the homework from the previous evening."
"For this session we reviewed topics we've covered before in preparation for the student's upcoming exam, which was moved to next Tuesday. We covered using the power rule to find derivatives, what it means for a function to be differential, writing equations of tangent lines, and the relationship between the graphs of functions and their derivatives. Next session we will continue with the graphs and begin to work on the product, quotient, and chain rules."
"We discussed her test over extremes, applications of differentiation, and optimization as well as the new material of related rates. She picked up on related rates well considering some of the previous difficulties with applications of differentiation. Her differentiation skills are improved, and she does well with deriving formulas to be used for multiple types of related rates problems."
"The student and I reviewed and worked on exercises covering the derivation of the natural log functions, logarithmic functions and exponential functions with and without base e. We reviewed also the chain rule, power rule, and some trigonometric concepts, like cosine, sine, tangent, and the unit circle."
"The student had a practice problem to work through today, which was focused mainly on derivatives. I tried to emphasize how important it is to think about derivatives as rates of change, and how we can use the fundamental theorems of calculus to solve word problems. We related derivatives to velocities and used the analogy of driving to make the point that integrating a derivative tells you how much stuff happened between the start and end."
"Today we went over proofs and an exam that was taken last week. The student seems to understand the ideas, but he's having some trouble with applying methods to write mathematical proofs. He has enough material to work with, and next week we will work together on how to write good proofs."
"The student and I worked through his math homework that covered related rates and implicit differentiation. For the most part he did well with the material, but he struggled with some of the harder related rates."
"The student is covering Riemann Sums in her calculus class. To begin our introduction to them, we discussed when using them is appropriate in real world applications, how to choose sub intervals, and when to sacrifice computation time for accuracy. We covered the four different estimation approaches, right hand, left hand, midpoint, and trapezoidal. I gave her problems with both defined functions and just graphs and had her estimate the area under the curve and then compare it to their perfect area using anti-derivatives."
"During the session, we covered implicit differentiation and proportional rates. The student was interested in learning the material and asked questions any time he needed to do so. We worked together on practice homework problems so he was left with his actual homework assignment to complete. Even though this was both of our first times using the online interface, I feel we were both able to adapt to it and use it effectively. I asked him to make a list of some of the most difficult subjects for him so that we can use our time covering the most important concepts first. I did not see any scores or grades to note the progress as this was our first session."
"During this session we went over solving triangles. This included using the law of sines and solving for ambiguous cases. The student had the most trouble understanding ambiguous cases and how you know how many solutions there are but after explaining it to her she picked up on it very well. She seemed to have complete understanding by the end of the session."
"Today, the student and I reviewed implicit differentiation, slopes at a given point, and the equation of the tangent line. She did very well with the material and only had a few stumbling blocks, but nothing of serious concern. Practice makes perfect. She has to be sure to practice as many problems as possible so that she gets the hang of things. I will be emailing a scanned copy of tonight's notes."
"Today the student and I went over some derivatives and antiderivatives involving trigonometric functions. Although he has not quite committed the more complicated ones to memory, he is able to identify pretty well. We also worked on some indefinite integrals that require him to anticipate the effects of the chain rule. After going through a few of these I think he has a better idea of what to look for. He also mentioned that Calculus has been going well for him lately, which I am happy to hear because I have seen a lot of improvement."