Recent Tutoring Session Reviews
"Today the student brought her review for a quiz that she will have tomorrow, over simplifying algebraic expressions that involve at most one step of combining like terms. Clarity was given to the meanings of the symbols used for multiplication, parentheses, and the small dot between two things two be multiplied, and the interchangeability of these two ways of expressing multiplication. Several problems featured both parentheses, and the dot, in representing the operation multiplication in a redundant fashion, apparently in an attempt to assess a student's ability to perform the correct operation and at the correct time. A majority of the time tonight was given to understanding how to simplify these expressions and at the end of the hour she was able to demonstrate this skill confidently on her own."
"Student had some homework to do that involved solving radical equations. She needed a quick reminder on how to do the problems, but was then able to do all of the problems by herself quickly and effortlessly."
"Last week the student and I covered primarily her science course as she had an upcoming exam the following day while we only spent about 15 minutes on her math coursework. I'm happy to say that the student received a 100% on her science exam which leads me to believe that our study sessions together are effective in familiarizing her with the concepts in that class. Today we worked on her math class since she has a math test tomorrow on Pythagorean theorem and scientific notation, topics that we briefly touched on at the end of last session. She had a worksheet that she had already answered and corrected in class that we worked on. I explained why some of her answers were incorrect and for the most part, it was small mistakes like multiplying by two instead of squaring, or moving the decimal to the left instead of the right. We went over these areas in detail so that she would not get them wrong on her exam. Afterwards, I gave her a review quiz on the questions as a sort of pre-test. We reviewed scientific once more before I left and I gave her an example of when the exponent would be negative and when it would be positive. Next week she will have received her exam score and we can go over any missed questions to see where she is at in the material."
"The student had made good progress on the problem we ended with last time, just needed a little nudge from me in the right direction to finish it off. We practiced more with double-sided inequalities and how to solve them for x. The student really got the hang of switching the signs when multiplying or dividing by a negative. The student demonstrated a good instinct for defining unknowns after reading the problem, and we were able to work through two problems well and really understand them. We then went over the basics of graphing inequalities- drawing the line itself, determining if the line should be dashed or solid, and deciding which side of the line to shade in. The student was doing well with it so we moved on to graphing slightly harder inequalities. This lead us into a general review of graphing lines given to us in the form y=mx+b. We spent a while on this, but the student got a good understanding of slope, y-intercept, and how to figure them out from slope-intercept form. We'll pick up here on Monday with exploring how useful it is to graph lines like this."
"We reviewed the student's homework assignment on the Fundamental Theorem of Calculus (FTC) parts 1 and 2. He has a good understanding of how to solve the problems in the assignments and didn't need much prompting from me. We went through the process of evaluating trig ratios of angles using the unit circle, which is important for getting correct signs (+/-). I also advised him on how to best format the evaluation of definite integrals to keep track of signs and reduce the probability of error. Finally, I explained to him, with function sketches of displacement and velocity, why and how the area under the graph is determined by using the anti-derivative. This essentially has no connection to any of the approximation methods. He is very bright and has good mental math visualization and is easy to work with. Overall, this was a very good first session. Future sessions will focus further on computational error reduction and the underlying concepts of integration."
"During the session, we reviewed some of the student's class worksheets that integrate the concept of the limit to find the slope of tangent lines at points along the curve. Though this sounds more like precalculus than it does like algebra two, he has approached this with a great deal of cleverness and is doing very well with the concept. We finished this pretty quickly, and decided to work for little bit. We briefly reviewed the ellipses. We then looked at some of his organic chemistry homework. He is doing very well; I hope to see him again soon."