Recent Tutoring Session Reviews
"The student has a good algebra foundation, so nothing lacking there, so calculus will mainly just be a conceptual exercise for him. He was able to do most of the homework with little help and a little guidance; topics include limits, continuity, and the two definitions/ uses of the derivative."
"The student and I covered topics from chapters 1 and 2 that will be covered on her first test this upcoming Wednesday. The session went well overall, but there was a lot of material to cover. She is having some trouble with graphing equations given hints about the limits and movements of functions around points. This is a common issue for many students. With more practice, she should be able to improve her ability to recognize certain functions and how to graph them quickly. I have encouraged her to work through the problems her professor emphasized as testing material. She has a great plan of attack and we will meet on Tuesday to answer more questions."
"Today's session went smoothly. We focused only on a few topics, primarily revolving around differentiation of functions, the basic rules or shortcuts to differentiation, and a couple of problems finding the equation to the tangent line at a point on a function's graph. The student has begun to get comfortable with differentiation functions in general. I told him that differentiation is like the arithmetic of calculus; in other words, it's probably the easiest part of calculus to master and likewise, it's the part of calculus everyone who studies the subject should know how to do without reference. I think with some more practice he should not have a problem with differentiation. After giving him a couple of practice problems, he does pretty well with finding the derivative to a function. He did better than I expected with his pacing and his solutions when it came to increasing the complexity of functions. He does a great job pacing his problem-solving on paper and breaking the problems up into manageable parts so as to accommodate his current ability to handle so many things happening at once. With this ability, he is able to come to the solution where I think some students would not. That's not to say he doesn't need more practice, but I feel confident he'll be fine in this class, and even more so as I work with him as well. Other than practice with differentiation, I spoke to him here and there for a few minutes on why calculus came to be, historically, and how the derivative relates to graphical concepts. This all mainly stemmed from his teacher's introduction to the fundamental theorem of calculus and how the derivative related to the area underneath the graph. This extended a bit to antidifferentiation/ integration because when understanding the fundamental theorem both integration and differentiation are essential. That being said, I was glad to see his teacher brought up the concept early. Understanding why calculus was invented, or discovered, in the first place sometimes helps students to understand how or why calculus is used with respect to practical concepts."
"The student and I continued doing calc II work. We reviewed derivatives and particles, velocity and acceleration. Lastly, we took derivatives and determined rates of physical processes."
"We went through some problems practicing finding derivatives of functions. We particularly worked with the chain rule and worked further with the definition of a derivative as a limit function. We also practiced finding tangent lines at a given point of a function. There is still some work to be done for the student to understand derivatives conceptually, but he is making progress. In practice, he is able to find the derivative of a function by several methods. He is eager to understand the material, and with practice will master it."
"We covered the product and quotient rules. The student was primarily struggling with trigonometric concepts. Despite any struggles, she seemed confident. One strategy that we covered was substituting using given information in product rule problems. I did not leave her with any extra practice. She continues to earn excellent scores on homework and quizzes. A win from this session was an understanding of how to approach problems dealing with given information."