Teaching Math

I haven’t posted for sometime because of a busy schedule — nine hours a week as an MA Economics student, and six hours a week as a Math lecturer at the University of the Philippines. I applied for a teaching position, and was accepted, because I wanted to try out teaching ideas which came to me while attending lectures as an MA student. I have written several posts about this.

I am now implementing those ideas. As usual, reality is much more complex than theory, although I believe I am moving towards a better teaching method and my students are responding positively to my novel approach.

Basically, I keep lectures at the minimum and make students spend most of their time solving problems. Instead of lectures, I give reading assignments, together with a set of problems to solve. I assign homework every class session and we do seatwork in most class sessions too. As I wrote in earlier posts, in swimming classes, it is the student, not the teacher, who stays in the water most of the time. In a Math class, the water is a blank sheet of paper. Lots of them. Instead of the teacher solving problems on the blackboard, I make the students solve problems on paper.

The advanced students caught on quickly. Among the low scorers, some have shown major improvements. But a few students still lag behind. I spend hours thinking how I can get the concepts across. At their current pace, they will fail the course. I (or, rather, they) need a breakthrough. We are nearly two months into the course, we have another two months. Sometimes, it simply takes time to sink in. I hope that is simply the case.

My biggest problem was that students tend to hide their lack of knowledge, instead of bringing it out in the open, so that we could do something about it. For weeks, we seemed to be playing hide-and-seek, with some students copying from classmates or using all the time-tested student methods for beating the system. The problem is grades. They have become a student fetish, separate from learning itself. Student will do all kinds of things, including cheat, to get better grades. It is not really their fault. The school system makes them do it. Instead of lectures, I simply explained on several sessions why it was important that students admit to themselves the lack of knowledge and to acknowledge it openly, especially to the teacher, instead of hiding the situation (unsuccessfully) from the teacher, their classmates and themselves. I think it took weeks for the message to sink in. But now, I think most have gotten the message, and we are ready for real learning.

Initially, I thought I could encourage my students to solve problems by using grades as the incentive: it was easy to get high scores in homework and seatwork because I encouraged them to ask for help from classmates, high scores which could pull up their final grades. I think it worked for some, but for others, the high scores became an end in themselves and some were getting them minus the learning that should have accompanied the high scores.

So, I’ve changed the approach. Now, homework are not graded by score but by effort. As long as there is an attempt to solve a problem, they get a point. If this creates another problem, maybe I’ll end up not grading homeworks at all. We’ll see.

In the meantime, it is gratifying to note that many students are responding to the method. What I need now is a breakthrough with respect to the few remaining low scorers. Just like swimming, maybe the breakthrough will simply come on its own time. I do hope it comes in time for their exams, not after.



  1. Posted September 14, 2009 at 9:00 pm | Permalink

    I’d just like to say that I admire how you paradigm shift on behalf of the students sir. There is no doubt that all your efforts have been for the sake of us, your students. I dunno. I guess I just wanted to say that. Hehe. The whole idea of unlimited make up exams is an offer I doubt other profs would give students. But you did. On behalf of the rest of the students(though they did not put me up to this FYI), Thanks.

  2. Josh
    Posted October 20, 2009 at 11:13 pm | Permalink

    I’ve read a number of your posts about teaching and I believe you have some very good ideas. One idea I would like to suggest is that you look into material that is available regarding the different ways that people seem to learn.

    There are many different ideas on this subject, but one of the systems that has been developed is called the “4mat system”. One of the websites that I found that gives a good overview is this one: http://www.geocities.com/jeniskanen/4mat.htm

    The basic premise of this system is that a student will fall into one of four quadrants that describes how they learn. The idea is that you teach the same way that you learn and that if you only teach to one of the quadrants, the learners that fall in the other 3 quadrants will have a difficult time learning.

    I agree that your way of instructing is different, and it sounds good, but, like the standard lectures, there are certain students that will understand it, and there are ones that won’t. As much as you don’t like the lectures, it is possible that some students learn best that way. Others may need the “time in the pool” to practice, while still others need to be given a “big picture” of how the math can be applicable to every-day life.

    For me personally, the way that I would see as a good way to learn would be the teacher starting out the course with a very difficult problem, let’s say it has to do with modeling the suspension system of a car. I realize that in the end this system would be best modeled using z-transforms and transfer functions, but that’s what you get to do when you follow the engineering path. The instructor could take an entire lecture breaking down that problem into it’s basic parts and then using the entire course to teach the basics related to that problem. The course doesn’t have to teach enough to do the entire problem, but they can get started on it. The students that like to work to an end goal, rather than just a grade then have a view of where all this stuff they’re learning could be used.

    Anyways, I’m very interested in what you’re doing and would love to continue this conversation.

  3. Anonymous
    Posted November 6, 2009 at 10:06 pm | Permalink

    I would just like to ask if you’re teaching Math 2 for the second sem of SY 2009-2010. I think I got you as my professor. 🙂

  4. Roberto Verzola
    Posted November 9, 2009 at 10:11 am | Permalink

    Yes, I’m teaching Math 2, TTh 830-10 and 10-1130am, 2nd semester.

  5. Hopeful Freshman
    Posted November 18, 2009 at 12:35 am | Permalink

    Good day! Is there still a slot in your Math 2 TTh 8:30-10 class?
    If there is, can I please prerog your subject? 🙂

  6. Roberto Verzola
    Posted November 22, 2009 at 10:30 am | Permalink

    Sorry, my two classes are already full.

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