Recent Tutoring Session Reviews
"The student studied for an exam on distance, rate and time. We used one of his review sheets. I reworked the questions and he completed them. Excellent session. He has a great understanding of the distance formula and can change the formula to solve for any one of the variables."
"Today we covered the rudiments of graphing equations, along with slope and y-intercepts. The student had two worksheets that he was assigned, and once he got the concepts, he made few errors. We agreed that I would set up a study room at the library for next week."
"Today, the student and I worked through her homework assignment, which covered graphing and transformations, and reviewed the quiz that I'd assigned to her. She excelled in graphing the translations. She initially had a few issues with labeling the axis and with calculating the translated points without a graph to look at. However, she was able to understand almost all of the concepts towards the end of our session. I left her with a few notes, which she is to study each day. Repetition of the topics studied today will help her. I will be sending additional notes for her to study based off of her performance today. She is highly motivated and will continue to grow steadily with practice. She did well today."
"We covered simplifying rational expressions and arithmetic operations with rational expressions. The student was initially struggling with factoring polynomials that had something other than a 1 as the leading coefficient. I showed her a trick to factor those, and once she understood that, she started to pick everything up much more quickly. I will be sending over a final that I wrote for Algebra 2 a few years back in order to see where any gaps in her understanding are."
"The student's class-schedule changes for this semester required him to switch math classes, and his new math class is still working on quadratics, so we reviewed the topic based on his class handout, which was to prepare the students for a quiz today. More specifically, we reviewed solving, factoring, and graphing quadratics and simplifying terms when working with exponents. We covered graphing more in-depth than the other topics because he forgot some of it (and he caught on quickly), as opposed to everything else in the handout, which he largely remembered except for more complicated applications, like factoring expressions with x-exponents greater than two. He struggles most with making minor mistakes. Sometimes, he even copies the problem wrong when writing it on another sheet of paper. I kept reminding him to be careful with his work. To try to reemphasize this another way, I let him work through a system of equations problem without pointing out that he made a copy error - forgetting to copy down a -1. The problem ended up having a "clean" answer (a whole-number integer). Afterward, I told him to check his work by plugging the x-value into both equations because he should get the same y-value for both. Because the same x-value yielded two different y-values, there must have been an error, so I had him review his work to find the mistake. After finding it, I explained how leaving out a mere -1 can change everything and that a clean answer doesn't necessarily indicate a correct one; in fact, the correct answer was a fraction. I hope that that hit home for him. A more minor struggle that he has is that he sometimes forgets that square-rooting yields two answers - the positive AND negative values, the latter of which he sometimes forgets. He seems to enjoy solving the problems and trying on his own before admitting that he's stuck. He knows what he doesn't know, which is great, and he wants to learn what he doesn't know, which is also great. For graphing, I taught him how to do it by just finding the vertex and x- and y-intercepts. When graphing a system of equations, I told him to circle the points of intersection, which he can see on the graph and solve for the exact values by setting the equations equal to each other. He was hesitant about graphing a system of equations for two parabolas because he was only used to graphing a parabola with a line, so I reassured him - and then showed him - that because he already knows how to graph a parabola, it doesn't matter how many he has to draw on the same graph because the same strategies apply. For solving for x, I taught him that the greatest exponent for x is the number of x-values when y=0. For factoring, he gets a little worried when seeing complicated terms with which he is unfamiliar, so I showed him how they're just applications of what he already knows, so there is nothing to fear. He remembered pretty much everything I've taught him, even after his long winter break, including the rule for factoring differences of perfect squares. He even remembered the rule that allows for, for example, x(x-6) + 5(x-6) = (x+5)(x-6), something that he didn't recall learning in class when I had taught him it. In fact, he had completed about half of the assignment before I had even gotten there, and all of it was correct except for a couple problems, which were only due to minor mistakes, not a lack of understanding."
"We went over some of the concepts involving trig identities and the unit circle. We discussed radians versus degrees and looked at the coordinates represented on the unit circle. We also discussed a few of his homework problems."