"The student has really improved with respect to her pacing in solving problems, beyond how she paced herself on problems when I began tutoring her. And her pace improvement definitely shows; she is able to pick up on new mathematical concepts and algebraic tools much quicker than she used to. Improvement in pacing trickles down into her other skills and so her problem-solving and understanding has bettered as well. I gave her a set of quadratic functions already in factored form and asked that she multiplies the factors out to write the quadratic function in standard form. I have eased her into using the "FOIL" method for doing this. The reason I mention this is because in many schools today, they are changing how students should approach these types of problems, instead of using "FOIL" they are using a "box" method. Though the student says she feels comfortable using the FOIL method already, I want to go over the box method as well next session. I want her to get to know both methods since I do not know which method her teacher will use come the time her class gets further into algebra. Afterward, I asked that she convert a set of quadratic functions in standard form into factored form. This can be a bit trickier than converting quadratic functions the other way around, so I helped her when she needed help here. But for the most part, she proved to be independent while solving these problems. Because I thought she was comfortable enough with these techniques for me to move on to the next topic, I introduced her to a third form in which quadratic functions can be written: the vertex form. Vertex form is just as important to understand as the standard and factored forms. This stems from the information given in a problem. She might encounter a problem that gives a few facts, and then asks her to find the equation for the quadratic function, but those few facts might not be enough to find the equation in standard or factored form. In this case, she will have to resort to vertex form. Again, I want to reiterate how well her pacing has improved. I cannot say what she's thinking, but her pacing shows that she is more confident with her algebraic abilities. That being said, she will need more practice with vertex form and this I will continue with during our next session, next Monday. I will continue to work on quadratics with her; they are a major topic of study in algebra 2."