Recent Tutoring Session Reviews
"In this session, we began by picking up on a related rate problem from the previous session. By this time, the student had already displayed some improvement in setting up the problems. The student did struggle a bit with recognizing the forms of certain formulas which is necessary to use the proper derivative method. We also went over a position, velocity, and acceleration problem and began a review of limits. Since limits and graphing are essential concepts in calculus, we will try to focus on these concepts in the forthcoming sessions."
"Today we looked at integration using the natural log function then discussed integration with inverse trig functions. We discovered the direct method, substitution, and dividing them into multiple fractions. The student will complete her homework assignments for extra practice after her lesson tomorrow. I have also asked her to review her previous quiz; we will review the types of errors she made next week. Otherwise, she had a great session and seemed to understand the material quickly!"
"We worked on the chain rule, product rule, and quotient rule of functions involving exponentials, square roots, and natural logs. We had worked on this over the summer so it was review, but it's been a while so we worked through many problems."
"We covered a few more optimization problems. We also focused on second derivative tests, intervals of concavity, inflection points, and how to determine them. Moreover, we learned how to draw a graph with given information like derivative at a point, second derivative at a point, interval of concavity, increasing slope, decreasing slopes, etc. We briefly started antiderivatives."
"We started covering questions as a review for an upcoming quiz. The student seems to struggle with the difference between differentiating, and integrating. She often starts the problem correctly, however she struggles to follow through to the end. She can grasp most of the calculus when she can keep it straight, but it's the algebra that is really hanging her up. Today the topics covered included algebraic rules for logarithms, and differentiating and integrating rational and logarithmic functions. She did all right with the substitution. I did get to see a test that she had recently completed. Her test confirmed the same struggles that she had been showing with me in our sessions."
"The student and I reviewed a previous exam to look at errors that involved left end behavior of functions and continuity. We went on to go over new material: definition/concept of the derivative; interpreting graphs of functions, their derivatives, and the relationship between the two; finding equations of lines tangent; and normal functions at given points. Almost all of the mistakes that the student made on her exam were small and indicated not paying attention--maybe she moved too quickly and didn't review before turning in her paper. She understands the concepts; I encourage her to review her work on exams and try to graph some of the simpler functions herself when doing her homework to get a 'feel' for their shapes rather than relying completely on her calculator."