What Is Math But Solving Problems? (Part 1)

Photo Credit: Neil Tackaberry Flickr via Compfight cc
Photo Credit: Neil Tackaberry Flickr via Compfight cc

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% 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.

 

Originally published in Sunstar Davao.

Email me at andy@freethinking.me. View previous articles at www.freethinking.me.

Adjusting the Sails

Photo Credit: PralineB Flickr via Compfight cc
Photo Credit: PralineB Flickr via Compfight cc

One of my favorite John Maxwell quotes is this: The pessimist complains about the wind. The optimist expects it to change. The leader adjusts the sails.

The reason I like this quote is that it captures a fundamental behavior that most people exhibit. Whether they are optimists or pessimists, non-leaders only react to a situation, whereas leaders act on it and can even turn seemingly hopeless predicaments around to their advantage.

In my more than 2 decades of being in different types of organizations, I have observed that all of them have their share of whiners, fans, and leaders. And true to the Pareto Principle, only 20% belong to the latter group.

Whiners are people who complain about anything. In a small group tasked to do an activity, for example, they complain about the rules, about the time limit, about the difficulty of the situation, and so on.  

In society, whiners complain about the politicians, religion, the weather, and so on, but they do little else. These are the people who seem to live their lives 24/7 on Facebook and Twitter. You see them ranting about this or that, or arguing with someone else almost every hour.

Whiners are also the masters of blame. They point their fingers left and right, and front and back. Everything is everyone else’s fault. “There are killings left and right. This is your fault Dutertards! Trump won. This is your fault evangelicals and protestants!”

In the meantime, one has to wonder what else they are doing with their lives besides being miserable on social media — which they self-righteously think is actually doing something to help the groups they think they are fighting for.

The fans are people who clap and cheer, but again also do little else. They loudly agree with what the leader says, but when they are asked to produce, they find an excuse to not do it, or they perform poorly. These are also times when they turn into whiners, complaining about this or that and giving different reasons why they cannot come up with the expected results.

Leaders are few because they are people who are willing to buckle down and do the hard work. And let’s face it, who wants to do the hard work, right? But leaders roll up their sleeves and do it anyway because they know what matters is not your talk but your walk. What matters is not just what comes out of your mouth, but what comes out of your actions. In fact, many leaders are too busy doing what needs to be done that they have little time for social media and all of the drama that goes with it.

A couple of weeks back, I had a chance to reconnect with Rev. Arnel Tan who was the officiating minister in a child dedication where my wife was the ninang (godmother). He is an old friend whom I have known since my teens. He is also a fellow columnist in Sunstar. We had a brief laugh over a mixup that happened a few weeks back. Someone at the proofreading or layout department was probably too stressed or overworked that he or she ran my column with Arnel’s name and photo. It was good that it wasn’t any of my anti-religion articles or Arnel might have gotten into hot water for “writing” such a piece.

When I submitted the article the following week, I included a reminder for the editorial team to use the photo of the bald guy.

Anyway, Arnel told me something interesting they have going on in the church. He told me that on certain days, I think it was Thursday and Friday, they open the church for medical missions and feeding programs. They have volunteer doctors and nurses over to help anyone who comes into the building needing help.

What was particularly interesting for me was when Arnel mentioned that he explicitly told his junior pastors, “When people come in, do not try to convert them and make them protestants. Just help them with what they need.” This, I think, is a very enlightened approach to the diverse mix of religions and cultures we have in our city.

This is one leader we have who knows how to adjust the sails.

Originally published in Sunstar Davao.

Email me at andy@freethinking.me. View previous articles at www.freethinking.me.

Parang Pero Hindi

Photo Credit: Aramisse Flickr via Compfight cc
Photo Credit: Aramisse Flickr via Compfight cc

There are some teachers I’ve had whose names I cannot remember, and there are some teachers whom I will never forget. Orlando “Orly” Darang belongs to the latter group. I heard the news that he passed away on All Souls Day.

When I was a high school freshman, I would sometimes go to the library and look at the old yearbooks. The teachers photos were usually accompanied by short descriptions. Mr. Darang’s description, year after year, usually began with “Tall, dark, and dark,” so that is how I first became acquainted with him.

He became my Filipino teacher in junior year and I found out that he was indeed tall, dark, and dark, with strong, muscular forearms to boot. He was a bit scary that first day of class, and he sternly warned us to always bring our copy of Noli Me Tangere, or face the consequences.

We later learned what the consequence was a few weeks later when one of our classmates forgot his book. He had to lift his chair over his head while Mr. Darang proceeded to lecture and discuss the lesson like nothing was going on. I don’t think I ever forgot to bring my book after that. I mean, if my house were burning, I would probably rush in to grab my Noli de Tangere so I wouldn’t have to face Mr.  Darang’s icy stare the next day.

As the weeks and months went by, the ice began to melt and we began to see his softer side. His one pet peeve was when students began their answers with “Parang” and he would be quick to interrupt with his famous line, “Parang pero hindi?” which usually stopped a student dead cold, much to Mr. Darang’s visible amusement. A typical dialogue would go like this:

Mr. D: “Ano ang ibig sabihin ng sinabi ni Padre Damaso?”

Student: “Sir, ganito kasi iyan. Parang…”

Mr. D: “Ah parang pero hindi?”

Student: “…”

(This dialogue gets lost in translation so I won’t even bother).

You would think that we would have learned to stop saying that word but no, almost every class there was someone who would inevitably say it only to realize too late when he or she was met with the dreaded “parang pero hindi?”

One day, one of my classmates, Raul, did the unthinkable and managed to parry that interjection. When he said “Parang…” and Mr. Darang promptly interjected with, “Parang pero hindi?” Raul didn’t miss a beat and answered, “Hindi sir. Parang pero oo…” and proceeded to give his answer, which no one heard or remembered because everyone was laughing, including Mr. Darang.

There was another time when Mr. Darang walked into the classroom and wrote on the board the words “oten” and “puke” in big, bold letters. There was some nervous tension in the room. Some girls giggled and some boys howled, and the word “bastos” could be heard muttered all around. Mr. Darang promptly addressed the issue asking why these words were considered as “bastos.” Was it simply because they were in Filipino? What if he had written “penis” and “vagina” on the board? Don’t we use those terms in biology class? So why does it sound clinical and scientific in English while sounding vulgar in Filipino? That was one of the classes which really made me think about the power of language and words beyond their dictionary meanings.

He was not all fire and brimstone and was actually very approachable as I would find out when it was composition-writing time. My closest friends know that Filipino is my “hatest” subject. I was a voracious reader of English books and I spoke Chinese and Bisaya at home. The only place I ever spoke Tagalog was in school so I always had a rough time understanding and forming words.

I told Mr. Darang of my difficulty and he understood my problem. He would gently coach me as I asked him how to say this, or how to say that, or what this or that word meant. I learned that underneath his seemingly hard exterior was someone who wanted to help. He had the heart of an educator who wanted his students to excel and perform their very best.

Today, more than twenty years after, I remember the life of a man who was one of those who shaped and molded me into what I am today, who is certainly much more than what I portrayed him to be in this meager piece. And as I pause and reflect on the brief intersection of his life and mine, it seems that I am just waking up from a hauntingly, beautiful dream.

Parang isang munting magandang panaginip…parang pero oo.

Paalam, sir.

 

Originally published in Sunstar Davao.

Email me at andy@freethinking.me. View previous articles at www.freethinking.me.

Much Ado About Mocha

Photo Credit: kendrak Flickr via Compfight cc
Photo Credit: kendrak Flickr via Compfight cc

Warning: If the mere mention of Mocha Uson’s name makes your stomach turn and makes you want to strangle the person nearest to you, please do not read on, for your own safety and for those around you.

The hot topic for this week in social media seems to be Mocha Uson and the petition to shut down her facebook page, Mocha Uson Blog.

A certain Paul Quilet started a petition at Change.org, a website that gathers electronic signatures from people and sends a formal petition to a key decision or policy maker. In this case, Mr. Quilet’s plea was directed to Facebook Inc., asking them to suspend the Mocha Uson Blog page, for the following reason:

Mocha Uson, a Filipino entertainer-turned-Duterte die-hard supporter uses her Facebook page to spread fictitious/unsupported claims, fake news, and false information about pressing issues in the Philippines, from the role the USAID plays in the country to news concerning government officials and other personalities, eliciting unwarranted hate from the public. The said Facebook page widens the rift between those who support the current administration and those who are critical of it.

The first reaction I felt was amusement. People critical of the president’s “dictatorial” regime now want to shut someone up and muzzle her. The irony is apparently lost on them.

The issue has then sparked an online debate on rights versus responsibilities and on freedom of speech, and has resulted in another round of name-calling, unfriending and blocking. Isn’t social media a wonderful tool for venting and for making you feel more significant than you really are?

I found some time to revisit the Mocha Uson Blog and found that I had “liked” the page, probably during the election period. I rarely followed it though and would just get the occasional update on my feed. I went through the wall that supposedly spreads misinformation and elicits hatred. I found little to warrant this extravagant claim.

Sure, she posts from informal websites and non-mainstream news sources, usually with the statement, “Eto ang sabi nila…ano sa tingin nyo, ka-DDS?” (This is what they say…what do you think, fellow DDS or Duterte-Diehard-Supporters?).  But she also posts from mainstream sources as well, and not everything she shares is fake or untrue or illogical or worthy of derision (which is the impression you get when you listen to her critics — and yes, I have a lot of them on my feed).

In fact, some of those who are criticizing her of “hate speech” and of “widening the rift” between administration supporters and critics would do well to examine their own posts about her and her followers. Isn’t calling people stupid, bobo, tanga, or mindless zombies also hate speech? How exactly are they helping to narrow the rift by doing that?

A few months ago, I got into a heated discussion with someone I didn’t know who was criticizing a friend of mine on his wall. Instead of just sticking to the arguments, that person combed through my wall and made fun of what was there, even mocking my glorious bald head.

Another person made a snide comment about my support for the president on what I thought was a totally unpolitical joke, and even called me a genocide apologist. Not content with that, she posted on her own page that I was a genocide apologist par excellence.

Wow! If someone manages to find this piece that makes me deserving of such an honor, please tell me where I can read it. I feel like I’ve won a Palanca award for literature without having to write anything.

Anyway, do I write a petition to have Facebook remove their pages? Do I report them for hate speech? No, I just leave them be. I understand that it is easier to despise others if you stereotype and dehumanize them.  I understand that some people are not yet mature enough to handle freedom, or that they are too blinded by their own bloodlust at pointing out others’ shortcomings to see the three fingers pointing back at them.

But that’s ok. I am, in essence, a hopeful person and I believe that humanity will one day wake up and see the overpowering force of love over hate, of joy over despair, and of acceptance over derision.

Originally published in Sunstar Davao.

Email me at andy@freethinking.me. View previous articles at www.freethinking.me.

Deadline Tomorrow

Photo Credit: woodleywonderworks Flickr via Compfight cc

Photo Credit: woodleywonderworks Flickr via Compfight cc

Deadline tomorrow!!! Everything you’ve ever posted becomes public from tomorrow. Even messages that have been deleted or the photos not allowed…I do not give Facebook or any entities associated with Facebook permission to use my pictures, information, messages or posts, both past and future. With this statement, I give notice to Facebook it is strictly forbidden to disclose, copy, distribute, or take any other action against me based on this profile and/or its contents…

If you were one of people who became genuinely concerned about your online privacy and reposted this message (even if it was “just to be safe”), then pat yourself on the back and greet yourself a Happy April Fools Day in October. There were apparently a good number of you as this recent viral trend made it to the news again.

“Again?” You might ask.

Well, yes, because this little prank or hoax has been around since 2012 (according to Snopes.com).

So let’s be clear about a couple of things:

  1. Facebook is not making all your posts public, and certainly not those messages or photos that have been deleted.
  2. Nothing you post on your wall, even if it sounds legalese, overrides the Policies and Terms Of Use that you agreed to when you signed up for a Facebook account. In other words, there were certain things you agreed to when you decided to get an account. Yes, it’s that long, boring blob of text that you probably skipped or hurriedly scrolled down to just to tick the “I agree” checkbox at the bottom.

Let me tell you about a tool that you can use before falling for these hoaxes again. But it really needs no introduction as  I’m sure you know the tool I’m talking about. It has been around far longer than Facebook. It’s called Google.

Whenever you see any of these things again, go to Google.com and paste a significant portion of the text. For example, you could copy the phrase “I do not give Facebook or any entities associated with Facebook permission” and put that into the Google search bar, and you will immediately see a number of links leading to articles that you can read and discern for yourselves whether it is true or not. Instead of copying text, you can also use key words. For example, “Facebook privacy hoax or not” also works.

Now, like I said, this is a tool and like any tool it needs to be handled properly. Not all articles you find on Google are guaranteed to be true. The next thing you should do is check the source of the article. Is it a personal blog, a relatively unknown newsletter, or a known news source? And then read the article itself. Is it an opinion piece or a fact-piece? Does it cite credible sources? And so on.

“That sounds like a lot of hard work,” you might say.

Well, of course it is. But why do you think a lot of people fall for pyramid scams and get-rich-quick schemes even if they have been around for decades? Why do people fall for rumors and false stories? Why do people believe in self-medicating with herbal remedies instead of getting proper medical diagnoses?

Getting to the truth is hard and involves some work and some thinking, but what is the alternative? Would you rather be fooled? Would you rather spread false stories? Would you rather suffer from complications because you took that concoction your neighbor boiled rather than seeking sound scientific advice?

You decide.

Originally published in Sunstar Davao.

Email me at andy@freethinking.me. View previous articles at www.freethinking.me.