Recent Tutoring Session Reviews
"Today, the student and I focused on an assignment for class. The assignment covered long division and also guess and check problems. The student and I worked on critical thinking by making informed guesses and the checking our answers using tools the student is familiar with."
"The student and I worked on the rest of her chapter 8 assignments, a take home quiz in preparation for her test next week. She has the material down fairly solidly (surface areas of rectangular and triangular prisms, volume of rectangular prisms)."
"Went over advanced series and sequences. The student already had a detailed understanding of the basics and the concepts of convergence. She had trouble comprehending the McLaurin and Taylor series and its application. I broke down her notes and showed how the basic model of the McLaurin series is applied to specific functions creating a power series. Once she understood the basics, I showed her how alterations to the function can be reflected in the McLaurin model. We then began reviewing the application in approximating the integral. It took the both of us a couple of attempts before we broke ground and comprehended the key behind it. After a couple more practice problems the student began to feel more comfortable with the material."
"The student and I had another great session yesterday. We started off with a two-step equations problem to review last week's material. She did the first one quickly and correctly using the substitution method. She used elimination method on the second problem and transformed and combined the equations perfectly but took a little time to figure out how to plug the variable she solved for back into one of the original equations to solve for the second variable. She did figure it out and completed the problem correctly. I've been encouraging her to correct herself when she accidentally says "subtract" instead of "divide" and she didn't make that mistake once today! We spent the remaining time going over factoring a polynomial into its roots, and what exactly that means in terms of how the polynomial looks when you graph it. We talked about multiplicity of a root, and what it looks like on a graph when you have a root of multiplicity two, three, or four. We also talked about the general characteristics of a quadratic, a cubic, and a quartic polynomial when they are graphed - what direction they start in, what it looks like when they cross the x-axis, and what direction they end in. The student caught on to these patterns and characteristics very quickly, and was able to graph equations like y=(x-2)(x-2)(x-4) and variations of that very well. We finished by graphing several variations of y=x^2. We looked at what happened to that curve when you increase the x^2 term, when you add a constant, and when you add an x term. My hope was that this would help her really understand the shape and features of quadratic graphs and equations. We will review this on Wednesday then do some work with equations - really exploring all the tools she has at her disposal to solve an equation for x. I really have felt in the last 3-4 sessions that things are really clicking and she is picking up the material and understanding it well. I hope she is also happy with her progress, and perhaps even enjoying solving some of these problems! She is good at figuring things out on her own."
"The student and I worked on determining the area of objects. He has a good introductory grasp of the concept, but has not mastered it. He had a little trouble focusing the first 30 minutes, but after some direction, he was more focused."
"The student's math and science teachers are allowing him to retake quizzes and tests from first semester. First, he chose to correct his math tests and quizzes, which is a condition of the retake. We first reviewed the lesson or chapter in the textbook, and then he moved on to correcting the mistakes for each quiz or test. Then, we moved on to science and followed the same process. Lastly, we reviewed the extra math problems I created from last session. He is getting better at dividing fractions. I created an additional set of extra math. I created and added an exercise, Complete the Chart: Fractions, Decimals, and Percentages."