Yes, I did try to teach algebra in 15 minutes, before a panel of about a dozen math professors at that of the University of the Philippines Institute of Mathematics.

In previous pieces, I had expressed frustration at the lecture-based method of teaching math and math-related subjects. Having gone back to school for an MA in economics, I strongly believed there was a huge room for improvement in teaching methods. (You can read those pieces here: “How I would teach Math“, “The only way to learn is to accumulate flying hours“, “The problem with lectures“).

I felt strongly enough about this matter that I did what seemed to some a very presumptuous thing: I applied for a part-time teaching position so I can implement the methods I had in mind. Prof. Joey Balmaceda of the Math Institute very kindly considered my application instead of rejecting it outright, and I was scheduled for interview and a demo lecture last Monday, April 27. About ten other applicants were also interviewed that day.

This is my “algebra made easy” 15-minute lecture:

Imagine a balance people use to compare weights. Yes, the same balance typically held by a blind-folded lady to symbolize that everyone is equal before the law. If you can understand how a balance works, you can understand algebra in 15 minutes.

Suppose I put an unknown weight on the left side of the balance and, by trial and error, find that a 5-gram weight (in the demo, I used kilos) balanced the unknown weight. Then, we can conclude that the unknown weight is 5 grams, right? Suppose I add a 2-gram weight on the left side, how do I keep the two sides in balance? I should also add a 2-gram weight on the right side. If I add a 1-gram weight on the right side, then I need to add a 1-gram weight on the left side two, to keep the two sides in balance. If I take 3 grams away from one side, then I must also take away 3 grams from tne other side to keep the whole thing in balance.

Like Lady Justice is supposed to do (this sentence occurred to me only now, I didn’t say this in my demo), both sides must be treated absolutely equally. If I triple the weight on one side, then I must also triple the weight on the other side. If I halve one side, then I must also halve the other side.

**Do unto one side what you would have done unto the other side.**

That, in essence, is algebra. Everything else is just details and tricks.

Solving algebraic equations is simply playing this game of balance. And that’s what we will learn the next time. (If I had another 15 minutes, that would have been enough to explain the process of solving for X.)

How did the panel of interviewers respond? They were very polite, but I also saw a few nodding heads.

I am keeping my fingers crossed.

Actually, I found it ironic trying to prove myself with a demo lecture (as required from all applicants), when in fact I spent the previous 30 minutes trying to convince the panel that my approach would be to minimize lectures and to maximize individual reading from the textbook and actual problem-solving with pencil and paper. My own demo lecture highlighted, for me, my point that lectures are a very poor way to implement the learning process. If it were a real class, I would have simply started by giving everyone a set of algebra problems, from the extremely simple to the moderately simple, and in addition assigned as homework a range of pages to read as well as another set of problems to work on, for submission in the next session.

In a lecture, I had told the panel, the lecturer learns more than the students. A math class should be run like a swimming class, where the instructor stands by the pool, out of the water, while the students are in the pool, learning how to swim.

In math and other math-related subjects, paper and pencil are the students’ swimming pool.

## 2 Comments

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