Author: Andy Uyboco

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My Love-Hate Relationship with Math (Part 2)

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Click here for Part 1.

So now I had a page full of word problems which I really hadn’t figured out how to solve in a coherent manner, and now I had to solve it using x and equations, which I barely understood at this point.

I was pretty desperate. This was before the internet so you couldn’t just go online and Google up a tutorial. I remembered my childhood friend, Arthur, 2 years my senior and studying in another school. Arthur was always winning math contests here and there so I thought he could really help me.

I called him up, explained my situation and he asked me right then to read him one of the problems, which I did. Then he told me to write some stuff down, never mind if I didn’t understand it at that point. Then he explained to me what I had just written down, and how it related to the problem. And as I was listening to him, and looking at the problems, and looking at the solution, understanding slowly dawned on me.

To this day, I cannot explain how it happened. One minute, I was a confused mess staring at a bunch of number problems, coin problems, speed problems, work problems and so on. The next minute, I was seeing them in a new light, suddenly understanding how to translate the sentences into equations, then solving for the ever elusive x.

It was like magic.

Arthur walked me through some more problems but this time, I was writing things ahead of him and checking with him if what I had done was correct. He made some minor corrections here and there but at that moment, I understood what it was all about, and the difference was like night and day.

When we had our next class, I was surprised to find out that I was the only one who had answered all word problems correctly. I always thought there were people in class who were miles ahead of me. I mean, I would frequently be in the top 10 list since my elementary days but I was never at the top 5 or thereabouts, so I always felt I wasn’t as smart as some other people who would frequently be in those spots.

My teacher noticed the difference that day and it seemed she looked at me in a new way. I was eager to prove to myself that I had really understood this. I attacked the next problem set with glee, mostly solving it on my own now. I still called Arthur for pointers, especially on new types of problems, but I had things mostly figured out now.

It was amazing how my understanding word problems led to my understanding of almost all the other aspects of algebra that I found difficult before. I made sense of simplifying expressions, factoring, and so on, and I think it was even at this point when I stopped counting on my fingers when multiplying 7×8. I started getting high scores in quizzes and exams.

A few short months later, my teacher selected me and a bunch of others to join the city wide Math Olympiad, competing with other schools. To my great surprise, I finished second place over all.

I felt good. I felt confident. I felt like a rock star.

Originally published in Sunstar Davao.

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

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My Love-Hate Relationship with Math (Part 1)

I wasn’t a bad math student. I had a pretty good understanding of it in my elementary years, but I wasn’t that fast in operations. I had trouble memorizing the multiplication table at the higher digits. If you asked me to do 8×7 for example, I would still have to tick off the multiples of 8 on my fingers: 8, 16, 24…and so on until I got to my seventh finger, then write down the answer — I would do that all the way till high school.

I remember that at the start of every year since around grade 4 or 5, I would have trouble remembering how to perform certain operations like adding, subtracting, multiplying and dividing fractions and decimals, or how to get the least common denominator (LCD) and how that was different from getting the greatest common factor (GCF).

Despite that, I was chosen to be one of a handful of “math-gifted” students in sixth grade though I didn’t really feel all that gifted. Looking back now, they must have been pretty desperate. We were asked to cut short our lunch break and come in 30 minutes earlier for special lectures on advanced topics. Again, looking back, was that really a reward or punishment for being “gifted”?

I don’t remember much from those classes except that I struggled to keep up and that it highlighted what I hated most about math — word problems. In all my elementary years, I never understood how to solve a word problem. There was no step 1, 2, 3 to it. At least when multiplying fractions, as long as you memorize the steps, you had a pretty good chance of getting the right answer.

But word problems frustrated me.

Oh I would occasionally get them right but I never felt confident with them and I dreaded seeing them in quizzes or exams. No matter how I studied, I couldn’t prepare for a word problem. Thankfully, teachers didn’t make exams full of word problems, and so I survived elementary mathematics.

Then came high school and the start of algebra. Oh my, here I was trying to remember how to properly multiply decimals and subtract fractions, and now I have to deal with x, y and z, and sometimes a, b and c as well? But given some time, I was able to make some sense of the algebraic rules although factoring left me confused for a good long while, especially quadratic square trinomials.

Somehow, I survived freshman algebra. Now on to my sophomore year.

We began with a review of the basics, how to perform operations with variables, the laws of exponents, and so on. Shortly after that, we were introduced to equations, and then our teacher handed us a page of homework to do over the weekend.

When I got the page, I was terrified. It was full of word problems.

Originally published in Sunstar Davao.

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

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Education and Reality

Photo Credit: World Bank Photo Collection Flickr via Compfight cc

If education was meant to prepare one for “real” life, then why is it so unlike reality?

Where else do you see people grouped together by age, then forced to listen and work on 5 to 6 different topics a day (on which they have little or no choice on the matter), and at which they are evaluated and labeled at the end of the year as either smart or stupid (though the latter is rarely said out loud nowadays — instead people say “needs improvement”)?

In a world where people are increasingly becoming aware of the power of free choice and personal responsibility, schools seem to be denying the number one freedom of children — the freedom to pursue their own interests. Instead, they are being told to sit through lectures that adults have deemed as important and basic (and yes, you do really need to know how to factor quadratic square trinomials, and you need to memorize the periodic table of elements, as well as the entire character list of Noli Me Tangere even if all you dream about is to become a world class gymnast).

Of course, one might argue that in the real world, you also often need to do things that you don’t like in order to achieve what you like. A good basketball player needs to put in a lot of work on his body, going to the gym, building up his muscles, stretching, exercising, having a proper diet, putting in hours of practice, and a lot these things may not necessarily be things he wants to do, but he has to do them anyway.

Well, yes, but it was the person’s choice to be that kind of player.

Did we ever ask if our child’s dream was to be class valedictorian at the end of their elementary or high school education? Or did we just sort of push them along that path? As parents, do we respect our children’s choices and ambitions or are they the vehicle to satisfying our own ambitions (or frustrations)?

I believe that if a person really wants to pursue something, he will simply see obstacles as challenges and will find ways to hurdle them by himself. If a person is forced to do something however, even a little hardship will be seen as a mountain too bothersome to climb.

The word education comes from the latin educere meaning to draw out. Ironically, education today is not so much concerned about drawing out but about stuffing in and cramming as much material as it can into our kids’ uninterested brains.

Good educators, however, are people who can draw out a child’s innate potential, who can assist and nurture them as they pursue their own interests. They know when and how to push, and they also know when and how to leave things be and let learning occur at the students’ pace. They understand that they cannot keep watering a plant the whole day in the hopes of making it grow faster. They would only succeed in drowning it. They need to leave it alone most of the time and just watch it grow. Sometimes the plant may need a little pruning here and there, but for the most part, there is nothing you can really do to make it grow faster.

Originally published in Sunstar Davao.

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

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A Fresh Look At Technical Analysis (Part 2)

My fundamentalist views on investment has left me floundering in cryptocurrency. Because, while it is possible to look at “fundamentals” in cryptocurrency — the development team, the project plan, the underlying technology and algorithms — a lot of it is still on paper and involves heavy speculation.

Just because the technology sounds good and solid does not mean that it will take off and fly with mass adoption. History is filled with examples of great inventions boasting technically superior features but were flops. You’ve all heard of Apple’s iPhone and iPad but you probably didn’t know that Apple already created a handheld device called the Newton as early as 1993, and it flopped, which is why you probably don’t know about it.

Aside from that, the cryptocurrency market is so volatile and subject to wild swings. A lot of people who knew next to nothing about bitcoin jumped into it as “investors” last year when the market swung wildly upwards, from around $900 in January to $19,000 in December. And then it began to drop, and drop, and drop to around $6,500 as of this writing.

So I decided to give technical analysis a shot and to study it seriously.

The first thing I learned was that while it seems what technicians do is study charts and graphs, those who understand what they’re doing are really studying human behavior. There is a cycle of hope, greed, fear, and regret that you must understand. The value of studying charts is not because they contain some magical patterns to unlock untold riches, but they tell a story of buying and selling habits. Understanding that can help you predict what is most likely to happen next.

The second thing I learned is to always trade with a plan, and to stick with that plan. What usually happens to people who do not have a plan is they buy when they feel like it, and then try to improvise along the way. Doing that makes you subject to varying emotions which will greatly affect your decisions. If the price swings high, you might be reluctant to sell and take profits, hoping that it will go even higher. If the price goes down, you might be tempted to buy more because “hey, it’s a sale!”

Trading with a plan means assessing your risk-to-reward ratio and determining if a trade is worth it even before entering it. And if you do enter it, then you have to put in certain safeguards in the trade so that if things do not go as expected, you can keep your losses to a minimum and live to trade another day.

Of course, you need discipline to execute your trade as planned. It does no good to create a plan, and then during the trade, you start moving your safeguards because of greed or fear or any other emotion.

The third thing I learned is to be happy with small wins. You can wait for that rare 200% jackpot trade. Or you can start making smaller but more trades at which you only earn 10% each. If you make twelve 10% trades, that will give you a compounded return of 214%, and it won’t be as difficult or nerve-wracking.

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

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A Fresh Look At Technical Analysis (Part 1)

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When I started learning about stock trading and investing 20 years ago, I learned that there were 2 approaches: fundamental analysis and technical analysis.

Fundamental Analysis (also called Value Analysis or Value Investing) is the study of the underlying business behind the stock, which meant one had to pore over annual reports, financial statements and understand the value of the business itself. The idea was that one could find a good stock that was currently undervalued at the current market price, maybe because there is a temporary setback or simply because people have not begun to notice it yet.

Technical Analysis, on the other hand, is the study of price movement — that is, by studying price charts, and how price goes up and down in the past, and the volume of transactions, one can make certain predictions on how it will perform in the future.

A fundamental purist is therefore one who does not care about price movement, except to check if the business is currently overvalued or undervalued at the current price. A technical purist, however, does not look at the underlying business. He believes that everything that can be known about a stock is reflected in its price, or how the market currently perceives it. So if one understands how to “read” the market, one can make intelligent guesses on whether the price will move up or down, and trade accordingly.

I used to be a fundamental purist. I looked up to possibly the most famous and successful value investor, Warren Buffett, who has consistently ranked among the top 5 richest people in the world for the past 2 decades. Buffett is known for his uncanny investments, spotting great businesses at bargain prices. He would later on buy entire businesses outright rather than just investing in their stocks. He is also known for disdain of technical analysis, having once remarked, “I realized technical analysis doesn’t work when I turned the charts upside down and didn’t get a different answer.”

So I looked at technical analysis with the same disdain, ranking it only a notch higher than reading palms or tea leaves. For all the technicians charts and graphs, I yet had to find successful traders with results like Buffett, or his mentor Benjamin Graham, or Peter Lynch, and so on. I used to troll people who do technical analysis with comments such as, “Well, here’s how I look at that chart. If it doesn’t go up, it’s going to go down.”

My recent interest in cryptocurrency, however, has forced me to take a second look at technical analysis.

 

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