Recent Tutoring Session Reviews
"We spent a considerable amount of time going over her algebra II worksheets and homework, and we discussed conjugates, inverses, quadratics, dividing rational numbers, imaginary numbers, completing the square, square roots, the standard forms and graphs of functions and equations, etc. We spent time reviewing how to graph, find points, the slope, vertex, x- and y-intercepts, minimum and maximum points, etc., of lines and parabolas. We also reviewed factoring, FOILing, multiplying negatives, and other concepts from the semester. She has a large amount to review, and she did very well on the points that we covered. She said she felt confident in her upcoming performance, and she agreed to study the problems on her homework, review sheets, and examinations in preparation of her upcoming exam. I believe she will do very well on her exams. She is a very quick learner."
"We worked on trig integrals, specifically trig substitutions. I assigned the student several problems to work. He is doing well."
"During this session we used the student's homework problems to launch discussions about methods for finding the volume of irregular solids using integration (and other closely-related topics). The first problem we looked at involved integrating a population density over an area to find the total population. This type of problem is very similar procedurally to the problem of finding the volume of a solid given both a base and a function for the height or depth of the solid above or below the xy-plane. He recognized this connection immediately, which is excellent. There were a few subtle conceptual details involved in the next question which forced us to slow down to digest the meanings of the different functions. However, once I articulated the correct reasoning, the ideas seemed to crystalize for him without much delay. I think that if he develops a healthy hesitancy and approaches these questions more carefully, he shouldn't have a problem owning this topic."
"We began with a review of the (x, y ) plane and how to plot points, topics which are new to the student. He is enjoying the challenge and is able to plot points in all 4 quadrants and on the x or y lines. I demonstrated simple lines such as x = 1 or y = -2, which are vertical and horizontal, respectively. I introduced the term "slope" which was not given in the K12 lesson. We then reviewed functions as a "machine" or rule, a concept which greatly helped him to understand linear equations and how to work with them. He worked in Lesson 7 Scatter Plots, which were familiar to him from the previous unit on statistics. I explained that graphs are (x, y) planes with information attached to the points, which he readily grasped. He scored 100% on the Skills Update quiz with support by choosing to divide for a word problem, dividing fractions (by turning them into decimals first), and considering unit conversions and mode as a measure of a trend in data. He scored 100% on the Lesson Checkpoint quiz, as he comprehends graphs strongly. Lesson 8 - Interpreting Scatter Plots came easy to him due to the real-world connections and, he said, by the way I explained them. He scored 100% on both quizzes. He understood independent and dependent variables, positive and negative correlations (slopes), and when there is no correlation in the data - visualized a function machine where no rule works. Again, difficult concepts became clear and this is partly due to his very strong prior knowledge base. When he tried to visualize negative correlation, he struggled a bit and asked good clarifying questions. He is looking forward to our next session when he will take the final assessment for Unit 11."
"The student and I went over a review for her assessment tomorrow, including factoring exponents, functions of x, and composite functions. The student has really improved, but still makes small mistakes that result in deduction of points. We will work on this more in future sessions."
"The student has a test on Friday so we used this session to prepare for that. Most of the problems on this test seem to be revolving around graphing trig functions. Overall, she was doing well with these problems, but had a couple areas of concern. The biggest one was using "b" from transformed trig functions. We drilled that aspect and touched on all the other topics on the test. I will be sending some extra practice problems."