Recent Tutoring Session Reviews
"We began where we left off. We went through proofs by induction. This topic was much easier for the student, largely due to the much more formulaic aspects of the induction proofs. After going through several of these, we went into equivalence relations, equivalence classes and congruence classes. I started by talking with him a little about the topics, what they were precisely, and how he thought about them. We then went through a couple simpler examples applying the general definitions of equivalence relations before moving into congruence classes and dealing with modular numbers (and the applicable proofs). After this we went into discussions of functions on sets, looking at injective, surjective, and bijective functions and the ramifications of such information. Also included discussion of composition of functions and the resulting information known about one function (or composition) based on what's provided. We finally went into briefly going through cardinality of sets, discussing things like countability and talking about different methods of proof for equal size among countably infinite sets (also a comparison between equality of sets proofs to identical cardinality)."
"The student and I worked on multiplication, addition and subtraction facts as well as fractions. He is great with recalling the 1's, 2's, 5's, 10's and 11's. He knows some of the 3's and 6's but struggles with the higher numbers. I taught him a trick to remember the 3's and 6's. We also worked on fractions. We used a note card and cut it into pieces to show that fraction means part or pieces of a whole. Making that connection helped him make better sense of what fractions are. We then added and subtracted fractions with like denominators. Over the next week, he will work on the 4, 6, and 7 multiplication facts. Next time we work together, we will continue working on multiplication facts and also do real world application problems using fractions."
"Today the student and I finished a practice test in his book and practiced some of the problems that he was struggling with."
"The student was already working on her current Math homework dealing with angles of triangles and intersecting lines. I coached her through the rest of the homework assignment. She seems to find plane geometry easy to understand, which is encouraging. Some of the makeup Math assignments are graded, leaving only a couple left. I had the student write into her tracker, a reminder to ask her teachers to update these grades so that we can know for sure what's missing and not. A couple worksheets that she still has in her homework folder will be turned in. I reviewed the upcoming project and assignment deadlines with the student."
"I reviewed a number of the student's past AP Calculus exams, and explained the corrective concepts and procedures to the problems that she had answered incorrectly."
"We worked on the student's history worksheet on Japan, studied for his science quiz on genetic disorders and worked on math doing the area of various trapezoids."