Recent Tutoring Session Reviews
"For the first session, introductions were made, expectations were discussed, and we looked at the student's grades to determine our starting point. Topics that we briefly touched on included odds/evens, factoring, and multiplication tables, as a means to evaluate her understanding. We finished up with me checking her homework, and informing her of which problems were in correct, to be completed after I left."
"When the student and I began, I first asked her a few questions to get to know her a bit (as this was our first session together). They were general questions about her schooling, such as how is new material presented to her (e.g. videos, tutorials, both, etc.) and how is she graded in her on-line class (i.e. do homework and practice problems count towards her grade or is everything based on scheduled assessments). Then, I asked her to show me where she was in the curriculum. She said the last thing she went over was Finding Rational Roots of Polynomials using the Rational Root Theorem. That being the case, I gave her a few of those problems to warm her "math mind" up a bit, and to check for understanding on my part. She seemed to be very well versed on the Rational Root Theorem and had almost no trouble at all solving the problems I gave her. Along the way, I showed her a strategy to help her identify all the roots of a polynomial. She had told me that she was good at Polynomial Division (which she had also recently learned), so I showed her that after finding one root of a polynomial, she could factor that out of the original polynomial, and re-start the process with the new/remaining polynomial. She seemed to like this option, and it helped us with her upcoming lesson as well. After that, we went over some new topics, such as the Conjugate Root Theorem. She picked this up very quickly, which she proved when I gave her three practice problems from her textbook and got them all correct. By the time she finished those three, we moved on to her upcoming lesson: The Fundamental Theorem of Algebra. Here, her teacher had notes comparing the graphs of different quadratic functions and their real zeros. I had her draw out a few examples, and we discussed why even though they are all quadratic functions, they do not all have the same number of real zeros. We finished the session factoring polynomials with roots that were rational, irrational, and complex. Here, I pointed out to her the benefit of using the Rational Root Theorem to start, but integrating it with Polynomial Division along the way. Finally, with these problems, I taught her the importance of putting the final factor equal to zero, in order to solve it as an independent equation and determine the final roots (whether they be complex, irrational, or a combination of the two). Her attitude was very positive throughout our session, despite working with some long, daunting polynomials. I advised her to grab some extra practice problems from her textbook if she would like to refresh before her next scheduled quiz; and, I gave her my e-mail address in case she does that and has trouble with something. This was our first session together. I would like to view her quiz/test on the material we covered today next time. I think the biggest win today was for her confidence. I think she left the session feeling ready for anything because she had performed so well during our time together."
"The student had new homework section plus a quiz and test coming up this coming week. She worked through homework problems that she was stuck on and I checked her work. Just a couple of minor errors and a few times of pointing her in the right direction. The remaining time was spent going over broad topics that the quiz and test will cover."
"1). We covered lesson 1.3 and lesson 1.4. Packet was given by the student's math teacher from her high school. We covered following content in the both of the lessons. Lesson 1.3: Vocabularies: obtuse angle, acute angle, right angle, straight angle, opposite rays, linear pairs, supplementary angles, complementary angles, vertical angles. Constructions: Copy given angles, Angle Bisector. Lesson 1.4: Constructions: congruent line segments, 2 times enlarged line segment, a parallel line through given point and parallel to given line, perpendicular segment through given point and perpendicular to the given line segment, perpendicular bisector. 2). The student cooperated really well, and learned thoroughly. She understood and practiced both of the lessons 100%. 4). We made a separate tutoring spiral note book. Geometrical vocabulary definitions in student friendly language. I do- we do- you do teaching strategy. Questioning, and use of Geometrical tools."
"Second meeting with the student. We are working toward final exam in Algebra II for first semester. We reviewed the material from last session relating to inverse functions and he aced every question I gave him. Today we covered graphing and visualizing functions to better understand them at the extreme values of the domain and range. We also began to review complex and imaginary numbers, another topic with which the student indicated he was very unfamiliar. By the end of the session he was comfortable with complex numbers and the definition of "i" and combining like terms. We also reviewed linear vs. quadratic equations and solving for the root(s) of an equation, especially the concept of a quadratic equation with multiple roots. He likes to make problems appear harder than they are but he seems to be gaining more confidence with the subject matter and is over-thinking the solution less as we progress through the material. We will meet again on Sunday and determine a pace that will allow us to complete the review packet in time for his exam."
"1. We reviewed the questions on factoring quadratic formulas that he answered incorrectly. Afterward, we started the topic of graphing quadratic equations, which he just started learning in class. We learned about finding the x- and y-intercepts for quadratic formulas and matching graphs to their formulas. 2. He seems like he genuinely wants to learn the work and he's learning the concepts and rules quickly. 3. I taught him some strategies to arrive at the right answer quicker in situations where he must resort to trial and error. For example, I taught him how he could figure out what the factors of a quadratic formula would look like depending on whether b and/or c are positive or negative. 4. Yes, I asked him to complete the rest of the practice questions on factoring quadratic formulas. 5. He completed the work that I asked him to do. He learned the rules for factoring the sum of perfect squares and the sum and difference of perfect cubes. He catches on pretty quickly and is becoming more confident in his work."