Sessions on Pre-Calc and GRE prep

A good tutoring day

Yesterday I had two sessions. The first one was to prepare an entrance placement test where the student wants to qualify for a particular Calculus course, so he is being tested on Pre-calculus. The second session was with two students who are preparing for the GRE. Both tutoring sessions were early in the afternoon at the same Starbucks.
In the pre-calculus session we covered a wide variety of topics. Every problem in the study guide was about a different subject. For example, we saw inequalities with absolute value, exponents, logarithms, function evaluation, subtraction of algebraic fractions, factoring algebraic expression and so forth. The difficulty level was not hard, and the student understood all the explanations, even when he had not taken math in about ten years, since high school.
In the GRE prep session we focused on Geometry problems, working out of the ETS book. We reviewed basic properties and formulas for parallel lines, polygons, angles, triangles, special triangles, the Pythagorean formula, square roots, perimeter, area, circumference, volume, and surface area.
Both sessions had a nice flow regarding the problems. We did many different exercises and we did not get stuck at any single problem. Yesterday was a good tutoring day.

Sessions in Trigonometry, GMAT and Pre-Calc

A busy tutoring day

Last Saturday I had three students. The first session was about graphing sine and cosine functions, high school trig. The second one was a GMAT prep session, and the third one was about circles and parabolas, pre-calculus.
During the first session I was partially awake, not very alert, so I had to do the problems myself, kind of slowly, organizing the data in a table format, just to have it all in front of me and to be able to see what’s going on with the series of numbers. I personally like to solve the problems this way, but I don’t like having to do it like that during a tutoring session. The reason being the students understand the reasoning and the results but they sometimes end up with this expression on their face, like saying “How am I going to do that by myself when I am all alone?” This time it was pretty clear though (the hot chocolate helped me to wake up).
The GMAT prep session was the first one for the student I met last Saturday. It was one of those talks when they fully see what kind of test they face, and all the amount of work they will have to do, and for a moment they seriously consider quitting. This is a good sign. The GMAT is not a walk in the park by any means. The student is better advised to expect a heavy workload and to make some sacrifices in their schedule. We covered the inevitable “What for?” question. I am always straightforward about it; the test is just a hurdle for them to win admission over other applicants. Math is the cheapest filter applicable in a mass scale. Then we worked on a few problems covering sub-indexes, recursive formulas, Venn diagrams, and volume and area formulas. We scheduled a two-hour session for next week.
The third and last session last Saturday also lasted two hours. We had several problems where you are required to find the center and radius of a circle given three points on the circle. It was a little frustrating for my student to see how vastly different these problems can be in terms of difficulty level, computational detail, and time consumed. A set of points forming a right triangle, with horizontal and vertical legs of even length is like candy, but when the problem throws at you points with decimal coordinates, and fractional values for the slopes of the sides of the triangle, you can fill three pages and spend almost half and hour with just one problem. This can set the student in a state of panic, you know? Just realizing how long and tedious it can get sometimes may be alarming for many. Some books are like that, with problem sets that escalate quickly in the difficulty scale. At least my student ended up with the idea that it may be hard but is not impossible to work these problems out.
After the three sessions I was fried, and hungry. I went to eat a tasty bread bowl of soup at the Quizno’s Sub store in the Renaissance Town Center, off of Nobel Drive.