The challenges of teaching
(First of three parts)
Right out of university, the first classes I taught were pre-calculus and intermediate calculus for science freshmen and sophomores, respectively.
Generally, I had good students who were focused in class and did their assignments. They were used to examinations with a bit of computation, a lot of proving and even more problem solving.
At the end of the semester, five to eight students in a class of 40 would be exempted from the finals, with averages of A.
I soon handled a plethora of mathematics subjects—linear algebra, probability, statistics, etc.—mostly for sophomores and juniors majoring in math, management engineering, physics, computer science, economics honors and the like.
Student performance varied mainly due, I believed, to a prior math background (some high schools are certainly more rigorous academically than others).
I taught higher math for a decade or so. On the whole, it was not taxing to deal with students since most had good study habits and were motivated to work hard. I keep in touch with many of my first students and was a ninang in their weddings or the baptisms of their children.
Talk with Doreen
The late Doreen Fernandez was not only my teacher in freshman advanced placement English but also a mentor and friend. A former food columnist of the Inquirer, Doreen would invite friends to dine with her (incognito) in restaurants to sample the fare.
Over one sumptuous lunch at the turn of the millennium, our conversation turned to teaching.
Doreen said, very simply, “The best teachers should teach the worst students.”
I told Doreen I did not agree with her. Didn’t the smartest teachers teach the hardest courses? Nobel Prize winners, for instance, taught only select graduate students and never handled undergraduate classes.
I said that in most universities here and abroad, lecturers handled the basics and top professors handled more complex classes.
How could top teachers teach students who struggle most, particularly in elementary and high school where subject coordinators sometimes did not want to teach at all? Many coordinators were good teachers but did not teach anymore when given administrative posts.
Doreen said that was why she would never accept the position of dean. She did not even exactly enjoy being department chair but felt she had to “do her duty” at least once (before the position rotated to someone else).
But even as chair, Doreen taught as many classes as she could, staying in touch with what was happening in the classroom. And she did not teach only graduate classes but also undergraduate, especially freshmen, every year.
Doreen said she became a teacher because she loved to teach. She enjoyed teaching the best (such as those in advanced placement) but also taught students in basic classes.
“I want to help struggling students do well, too,” she said.
College algebra
Inspired by Doreen, I decided to shift my teaching focus to nonscience majors. In 2000 or so, I decided to teach basic math courses, college algebra in the first semester and finite math in the second, both geared toward nonscience students.
The math content was basic compared to the higher-level subjects I used to handle. My preparation was not so much on math content but on pedagogy.
I focused on giving students a wide range of detailed exercises (only practice can help nonmath-inclined or math-phobic students improve). Instead of having students do integration techniques or statistical tests manually, I encouraged them to use the scientific calculator or MS Excel when possible (except for arithmetic exercises, such as calculating percent or multiplying small numbers, which I demanded they did mentally).
I got frustrated at times when students found it hard to do basic math or exercise ordinary math sense. I despaired over answers such as “-7.5” (to the question: How many ways can you arrange 3 girls in a line?) or “52 percent” (to the question: If a bag that originally cost P1,000 is now worth P800, how much discount, in percent, would that be?).
I would ask the class to explain how and why their classmates came up with out-of-this-world answers, or to spot errors their classmates made on the board. Exemptions were rarer in these classes and I rejoiced if two or three students (out of 40) got a final grade of A.
Several times, I yearned to go deeper into say, higher-order polynomials (especially functions of degree 3 and up) but because students could barely deal with lines or parabolas (linear and quadratic functions with degree 1 and 2, respectively), we had to barely skim the surface.
When students demanded that math be applied to real life, I would tell them they did not know enough math yet to appreciate the beauty of more advanced topics.
I would tell them about the environmental applications of partial differential equations, for instance, which got them all excited.
But, realistically, how could we tackle differentials (a part of calculus) if we were stuck in basic algebra?
So, which is more challenging—teaching complex math to mathematically inclined students or teaching basic math to those who don’t exactly like the subject? I have done both and, believe me, the latter is much, much more difficult.
Motivation
Don’t get me wrong. Many of my humanities, social sciences and management students in college algebra pay attention and study well. Just because they are not science majors, does not mean I do not challenge them. I tailor my lectures to what I believe the class can achieve.
If I handle a class of prepared students, I often go beyond the required topics and give problems to make them think deeper. This is different from the way I treat a class of math-phobic students, where I would spend more time doing routine exercises to ensure that, at the very least, they pass. I have no illusions that I can make them like math but I hope that, at least, they will not hate it that much.
(To be continued next week)
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