Sunday , June 24, 2018

Uyboco: What is Math but solving problems? (Part 1)

THERE is a problem with math education today. I wrote an entrance exam for applicants of our company, a drugstore chain in the city.

The exam was designed to test basic knowledge and real-world problem-solving skills. Part of the exam are questions like, if this medicine costs 4.75 each and a customer buys 18 tablets, how much should he pay?

The most difficult question involves the item having a discount, and then asking how much change the customer should get if he pays with a large bill.

These are questions high school graduates should have little to no difficulty in solving (and yes, we tested it on some college students we know and they managed to solve them correctly). Yet we have many applicants who are supposedly college graduates who cannot answer the questions correctly. In fact, less than 50 percent of our applicants manage to pass the entire exam.

The problem, I believe is that math education has been too much focused on making students learn the how and not enough of the why. There is too much focus on skills and not enough on the purpose. A question most students ask about math is “What’s the use of this in real life?” and it’s a question math teachers brush aside or answer with some vague and useless reply like, “Oh it’s very useful. You’ll understand when you get to college.”

That is sad and unfortunate. Math teachers should pay more attention to that question. It should not be taken lightly. Answering that question satisfactorily can turn a disinterested student into an eager lifelong learner.

There is a Filipino saying that goes, “Kung gusto, may paraan. Kung ayaw, maraming dahilan.” Meaning, if you want something, you will find many ways of doing it, but if you don’t like to do something, you will also find many excuses not to.

Most students don’t understand why they’re doing math so they end up despising it because it is “useless” and a “waste of time.” They learn skills without knowing their purpose and thus easily forget them. The key is to get students to know why they’re doing something, and then they will become interested, and not only remember how to do it, but find even better and more innovative methods of doing so.

In our house, I am the designated Math tutor and I always have a hard time with my 12-year-old son. Previously, I thought that he was just not as capable as his siblings. But recently, he developed a keen interest in playing with Rubik’s Cube. He followed some tutorial videos on YouTube and he can now solve the entire cube very quickly.

I, myself, have never managed to solve more than one face of the cube at a time and I had to ask him to teach me. Then I told him, you know you’re already doing Math with this. It’s all about understanding what the blocks look like now, then how you want it to look, and then taking the necessary steps to get there.

“What is Math but solving problems?” said Dr. Norman Quimpo, a professor at the Ateneo de Manila University. So simple, so true, yet it is an assertion that many math teachers fail to grasp. They spend so much time teaching students to compute by hand that they have little time left teaching them how to understand the problem and how to understand the answers.

When I was teaching algebra, for example, I liked to stress that solving for x does not mean you have answered the problem. Sometimes, the answer to the problem is not the answer to the equation. And sometimes, you can even solve the problem without solving for x.

One of my pet peeves is having teachers who stress only one way of solving a problem. That is such a narrow-minded approach. Math is not about knowing the "proper way" to solve a problem because there is no such thing as a proper way. Rather it is about understanding a problem and then finding a solution to it and the solution may be more ingenious than you think and should in fact be celebrated rather than marked as wrong.

I remember in grade school, when my brilliant classmate Anthony Montecillo, proposed an alternate solution to a problem that the teacher had given. Instead of insisting on her method, our teacher invited Anthony to go to the board and explain his solution, which turned out to be faster and more intuitive than the “standard” method. Our teacher then praised the solution and dubbed it and said something like, “Oh, we should include this in our math books and call it the Montecillo method.”

Oh, if all teachers could be like that.

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