Recent Tutoring Session Reviews
"The student has a quiz on exponential functions and their graphical representations. He had a rocky start where he forgot most of the related concepts. Hence I asked him to use his notes to help him, while asking questions to challenge him to think and analyze. Through the process, his memory refreshed and did quite well in the end. We didn't have time for reviewing of his physics quiz. However, I asked him to use the test review sheet that we finished over the last session as a guide for a self-review."
"The student has a math quiz coming up on roots (i.e., rational exponents). She sometimes has trouble with when to multiply and when to add, so I thought this topic might be pretty tough for her. But she was actually really good at it. She knew exactly what to do to the exponents of variables. At first she had a little trouble with simplifying the numbers in front of the variables. She learned to use a factor tree and find groups of two, but that way takes a while and it gets more complicated with cube roots and fourth roots. She gets to use a really handy card with a table of powers on it, so I showed her how to look for factors in the appropriate column. After a couple of tries, she had it down. I also helped her with taking the root of a product or quotient, and she didn't have much trouble with that."
"The student had two homework sets. We first looked at the Taylor series problem. I explained their application and graphically showed what the Taylor series was so that she could better understand the error between the series and the actual function. We moved on to vectors, where I went over two methods for graphical addition and subtraction of vectors. She was struggling with using the dot-product to determine angles between vectors, but after several problems, felt comfortable with the methodology I showed her. I briefly introduced cross-products before she will go over them in class."
"This evening's session consisted of continuing to work through the student's exam review materials covering quadratic functions. We focused on practicing situation-based application problems as well as solving inequalities. Today I noted that he is very competent using the quadratic formula to solve equations. By introducing a graphical approach to inequalities, he seems to have a better grasp of what solutions to inequalities really mean. I assigned him to work through as many of the review problems on his own tonight, and plan to focus on even/odd functions at our next session tomorrow."
"Today the student and I began by discussing how to use trig to solve triangles that are not right triangles, which is what he is currently learning in class. He did not have any trouble with this once he learned how to use the law of sines. Then, we reviewed some of the topics we covered last week, especially how to find co-terminal angles. He understands how to do this fairly well when using degrees. We spent some time drawing pictures of angles and looking at how adding 360 degrees or 2pi radians brings you back to the same angle. Lastly, we looked at how to determine the trigonometric functions of an angle ending at a point on the coordinate plane."
"Today's lesson covered the evaluation of volume integrals using the area of infinitesimal slices. The student began our session with apparent trepidation, but quickly warmed up when she realized it really was a retread of concepts we already went through. Visualizing these kind of problems can be difficult, but we went through everything step-by-step and she got the hang of it. There is one more chapter test before the exam."
"During our session today, the student and I reviewed concepts she would need on her final, and I helped her identify when to use each concept. She showed great improvement over the past few sessions, and today we mostly worked on the problems she had not been able to complete herself, or the concepts she was still having issues with."
"Today we went over a few remaining problems from the practice sheet for exam 2. Major topics included advanced derivatives (multiple rules applied simultaneously, such as chain rules with product rules inside them, with further chain rules inside of them) and advanced limits."
"The student and I continued practicing evaluating limits today, using limits to define continuity as well. We also looked at sequences and series. She appeared to pick up all of these concepts quickly, with little repetition needed, but we will see if that holds on her homework this weekend."
"The student and I met today to go over limits, sketching a curve and optimization. Since the curve sketching problems take quite a bit of time to complete, especially with a lot of explanation, we mainly worked on these problems to get him familiar. I brought my textbook to go through the different steps and showed him a method using a number line. We worked on graphing a few cubics and a quartic as well as going through why each step is done and how to deal with imaginary roots. He felt like this approach did help him understand graphing more. He is going to send me some of the limit problems so that I can look over them before our next session. Also, we will try to hit on optimization problems."
"We covered the basic principles of calculus, including the first two chapters on limits and differentiation. We used curve sketching as an exercise to incorporate all of the topics reviewed today, and we went over several definitions and explored them more rigorously. The student seemingly struggles to keep up in a fast-paced, condensed summer class, which we remedied by doing several practice problems from a few different approaches. We discussed our topics for the next session, and we will spend a portion of the time to work on homework from next session onward. Overall, the session went very smoothly."
"Today we went over functions--domain, range, absolute/local minima/maxima, concavity, slope, etc.-- as well as how to model situations with those details. He struggled a bit with concavity and the idea of decreasing but not negative, but I think that was attributable to the fact that he had it entirely reversed. The student understood the method. He was noticeably quicker today at grasping ideas. I left him with a worksheet to complete for next time."