Recent Tutoring Session Reviews
"Today the student and I covered some earlier calculus material that he had found out was going to be on his upcoming test. We went over polynomial long division, asymptotes, and degrees of polynomials in relation to their asymptotes. He seems to have a decent understanding of these subjects, and I left him with the task of going over this material in preparation for his upcoming test. We will meet on Thursday and I will go over these subjects again to make sure he got a good grasp on them, and to make sure he is well prepared for his exam!"
"We worked on finding points of discontinuity and determining which type of discontinuity it is (jump, removable, etc.). In addition, we worked on determining whether it's left or right continuous. The student has made great progress on this. During this session, he demonstrated that he is really grasping these concepts. I think moving into the slower paced class is going to help a lot."
"The student's teacher gave an assignment over exponential differentiation before covering it in class, so before we started, I explained those rules. He understood the rules quickly, but some application questions threw him off at first."
"We focused on the student's chain rule homework. She struggled with using the chain rule initially due to the nature of the problem. With more simple problems she was able to use the chain rule correctly after some thought. I showed her the way to think of the chain rule in terms of fractions (i.e., d/dx = (d/dv) * (dv/dx)). This seems to have helped. I will make sure to have her evaluate a less difficult, but involved problem next time we meet. We should get back her first exam by next session!"
"We covered materials that are going to be on his test this Thursday. He seems to understand the material well enough. However, he struggled with solving using the chain rule and logarithm. So we mainly worked on that, as I gave him problems of varying difficulties. We also acknowledge his tendencies to start overthinking problems and complicate things for himself once the problems look complex. Overall, his conceptual understanding was good, but he just needed work on his problem solving."
"The student and I worked through his calculus homework which covered more exponential growth and decay. He had a better understanding of how to approach the various types of problems. The problems themselves did not have any calculus but he still understood the material."
"We covered logarithms and exponentials today. The notation is new and somewhat complex. We also covered inverse functions which were picked up quite easily. As before, the student does a lot of the work by himself with prompting only when needed. He just needs to isolate y and do arithmetic operations to get it to order of 1."
"We began using the limit definition of a derivative to start generalizing a formula for taking the derivative of a few specific type of functions such as a constant raised to the power of x. We practiced using the various rules for taking derivatives of functions such as taking the derivative of a constant function, taking the derivative of a function multiplied by a constant, and taking the derivative of a function that is the sum or difference of two functions. We also talked about what certain calculus terms mean, such as differentiable, tangent line, and derivative. I also identified specific sections in a supplemental textbook that have more examples and problems that the student can work through in parallel with her class text for more practice. We also went through strategies for approaching a math problem and how to begin solving. Once we translate what a problem is asking for, the student does well applying calculus concepts to solve it."
"I went over the chain rule with the student working several problems until he had a good method for working the problems down pat. We also worked some problems involving rates of change, and optimization problems. Overall, he seems to be very prepared for his upcoming test."
"The student wanted some additional help this week with anti-derivatives. We covered practical applications of anti-derivatives, applying them to kinematics and flow problems. We discussed independent variables again and how we can use them to form a dimensional analysis."
"The student and I looked at some calc problems involving transcendental functions and inverse trig functions. We also looked at some elementary differential equations. The student does well at setting up differential equations, but he is a little confused as to what makes them different from integration problems. It's mostly a notational concern, and we talked about it to the point where he feels he understands it. I'll keep an eye out to see if his confusion on this topic returns. Regarding the way he works through problems, he has made a great improvement in organizing his work."
"We covered implicit differentiation, the product rule, algebraic simplification, and differentiating trig identities. The student had a test the following day and seemed very well prepared. He prepared well before our meeting. He understood the concepts and just had a few hurdles, but was mostly able to work through them on his own."