Maybe I shouldn't have started this blog now, not with everything that's been going on.

In my Mathematical Methods 1 class last Tuesday we had a recitation slash board work review for the comprehensive exam two days later. We combined all the questions from the quizzes into one file, renumbered, and found out there are ninety nine items in all, which makes it an average of eleven problems per quiz.

It was just their good luck if they recognized the questions as being one of the few that he had answered in class during some of those sessions immediately after the quiz, and if they had it in their notes.

For the comprehensive exam itself, I suggested that we don’t give any word problems, and my co-teacher David, handling the other class, agreed. There were 27 items in the exam, going from simplifying exponents, dividing and adding rational expressions in one variable, removing radicals in the denominator (along with complex numbers), finding the value of a variable in rational expressions, involving absolute value, and in two and three- side inequalities.

There was one question on getting the line perpendicular to another line whose equation was given, as well as an inclusive point. One problem each was allotted for systems of equations in two and three variables, and involving quadratic equations.

One item asked for partial fractions, two on arithmetic sequences, two on geometric sequences, two on binomial theorem and two on exponentials and logarithms.

At more than twice the length of the average quiz, it wasn’t expected anyway that they would be able to answer everything. But at least there was an equal opportunity for them to get high on the topics that they know very well, assuming there was at least one, that is.

At the very least, afterwards they knew what to expect for the finals, which had the same coverage. For this reason I let them take home the questionnaire, which is becoming standard practice for me anyway.

In my Trigonometric Applications class, we took up the last topic, which is Law of Sines and Law of Cosines.

I used a method of teaching that I only resort to sparingly, and which is discouraged by the person who gave us a seminar on classroom effectiveness last May. I filled the whole board first with the concepts, formulas and examples before I started the discussion.

Part of the problem with this is that even after finishing writing, I still have to wait a few minutes when a lot of students complain that they are still copying.

Also, explaining what is written on the board partly knowing that some of them with a faster comprehension could already be reading ahead and not listening to a word I say had me preoccupied. Since I did not have to pause to write anything on the board while explaining, the pace of the lecture also became a bit fast (also due to the fact that a lot of time had been wasted waiting for them to copy).

Good points of the method: I’m assured I get to jot down everything I believe the students need to copy for the lecture, and that there is a comprehensible flow.

That’s all the time I have for now. Class dismissed.