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

Last Monday I started my Mathematical Methods 1 class with giving the students the opportunity to answer the questions from the quiz again, this time of the board and graded.

Some of the students still hesitated answering, giving the excuse that they weren’t able to answer the same question during the test. I told them that it was exactly why I was letting them answer it again, so that they could make up for whatever mistakes they may have made during the test, with the added help of having their notes open and being free to ask help from their classmates.

What I didn’t expect was that it was on the very first question that the student I asked to answer already had difficulty and he finished even after all the others who started at the same time.

Same with those who answered the problems using the graphical method, for whom I had to step in and show them how they could verify their answers there by using the other methods.

We had finished nine of the ten problems in the quiz when I decided that we had used up enough of the class time on the review, and that we should already proceed to the new lesson that David and I had decided on earlier.

This was solving now systems of (three) equations in three variables.

I asked them if they could use the graphical method for this. Of course they couldn’t, unless they get their hands on three-dimensional paper or they use computer software to simulate the lines and planes.

So we proceeded to the next method, which is elimination. For this they use two of the three equations to eliminate one of the three variables. Then they had to do the same for two other equations, eliminating the same variable as they did in the first instance. This would give them two new equations in two variables which they had to solve the same way as they did in the quiz.

From there they would substitute the numeric value they obtained in one of the new equations they made to get the other variable. Then they had to use these two variables in one of the original equations to solve for the variable they first eliminated, and not necessarily by the same method of elimination.

So not for the first time, they had to recall earlier lessons to be able to proceed with the current lesson.

The second method we discussed was still the same as in the preceding topic, which is substitution method. They had to reform one of the three equations to isolate one of the variables on one side. Then they had to use this to take the place of the same variable in the other two equations. From there they had to proceed like two equations in two variables again.

I announced that the next topic was determinants, and they asked that it be postponed to the next meeting, to which I was amenable. At least if gave them enough time to solve for the exercise I gave them.

That’s it for today. I’ll continue tomorrow. For now, class dismissed.