A business blog by an MBA graduate who's currently no longer interested in getting a Ph.D. This blog aims to share insights into the business world such as investments, economic policies, and more. Feel free to poke around, and learn more about what I have and want to say.
Search This Blog
The Solution for Better Mathematics Isn't a Homework Overload, Not Especially During the Holidays
IgnitED
As Christmas vacation comes near, I remember a couple of stuff why "vacations" aren't vacations. The schools tend to give ridiculous schedules. For example, the unit test or the periodical test comes right after Christmas vacation. Many times, the value of rest is overlooked. It's even ironic how science teachers should say, "Nobody should be sleeping at 9 P.M. You are in high school and you should sleep even at 10 P.M. Do your work even if it breaks your biological clock." Remembering those words, I also wrote an essay on why sleep-deprived education is one of the biggest problems. Then we wonder why students end up rebelling by doing many things like too much screen time (which I did a lot to the point I lost touch with reality) or even going out with the wrong people. I wonder if the three musketeers back in high school went home late out of rebellion? Sure, they weren't the unruly crowd but they probably did some mischief out of frustration.
I recall getting mad on Christmas breaks because I still had to do math drills. It's the most abused solution whether the teacher is good or terrible. Math homework is often said to improve math skills. High grades may be achieved in the short run. However, the irony of grades over learning is that good grades can't be maintained in the long run. Good grades should be a product of diligence and good character, not a result of cheating. When there's learning, better grades will follow and be more consistent than just grading alone.
Connecting mathematics to real life
How often teachers would give assignments over the weekend and the holidays. The body may have a fight-or-flight response. That may explain why some schools have a high failure rate. There are 40 students in Grade 5 but more than half failed. When people enter the first year under K+10, there's also the issue of 10 out of 30 didn't make it. Sure, it's good to raise parental concerns. It's a good thing though that some parents pulled out their children if they can't make it. In fact, I rebelled by playing video games for more than two hours. Even worse, family fights happen when I say, "I'm sick and tired of it! Just get over it! I'm stupid and I'll never be smart! What can I do? I'm stupid in math!" What's worse is that the Boomer Generation can be so proud of their academic accomplishments but their common sense has gone to zero. Today, schools tend to produce idiots more than intellectuals (read here).
The problem with teaching mathematics is always rooted in this--it's not linked to real-life scenarios. I almost thrashed out at DNews, until this video by Trace Dominguez came...
Dominguez discusses the one thing that really makes sense. In his case, there's no such thing as a math person--most people feel stupid because mathematics is taught stupidly. I cringed when he presented the sad truth that we're taught only how to do math but not to understand it. This makes me think that homework overload isn't feasible. But no, the education system tends to demonize rest and relaxation as "something evil". Even worse, parents want to get their children to be early graduates. It's almost like trying to force a plant to grow with an overdose of fertilizer.
Lockhart begins with a vivid parable in which a musician has a nightmare in which music is taught to children by rote memorization of sheet music and formal rules for manipulating notes. In the nightmare, students never actually listen to music, at least not until advanced college classes or graduate school.
The problem is that this abstract memorization and formal-method-based "music" education closely resembles the "math" education that most students receive. Formulas and algorithms are delivered with no context or motivation, with students made to simply memorize and apply them.
Part of why many students end up disliking math, or convincing themselves that they are bad at math, comes from this emphasis on formulas and notation and methods at the expense of actually deep understanding of the naturally fascinating things mathematicians explore. It's understandable that many students (and adults) get frustrated at memorizing context-free strings of symbols and methods to manipulate them.
This goes against what math is really about. The essence of mathematics is recognizing interesting patterns in interesting abstractions of reality and finding properties of those patterns and abstractions. This is inherently a much more creative field than the dry symbol manipulation taught conventionally.
During the preparations for the NSAT (which were thankfully canceled), I could remember coercing one of my former enemies to recall his mathematical genius. Sure, he was known as a math wizard but even he soon suffered from stress. I wonder if some of his silly written work resulted from a flight-or-fight response. I was good at writing and he was good at mathematics. Both of us were weak at each other's strengths. That's why we were told it'd be better if we both cooperated.
Teaching mathematics in Chinese classes feels redundant. However, I talked with someone who graduated high school in Chinese education saying that Chinese mathematics had better reasoning. I got so curious that I researched on Chinese mathematics and wrote an essay about it (read here). I was even amazed when I found Domino Chinesediscussing how Chinese mathematics is winning. The Chinese mathematics method can be learned without learning Mandarin. It can be taught in any language. We don't learn Greek to learn mathematics pioneered in ancient Greece. Isaac Newton didn't need to learn Greek before he discovered how calculus (invented by Hippharchus) could be used in his experiments.
I think this also shows how mathematics can be used by any country:
The pedagogical approach to teaching Mathematics at schools in China is known as the Mastery Method, and there is a lot more to this approach than simply memorising times tables.
A central concept in the Mastery Method is the development of a solid foundation in basic Mathematics ability. This is established by focusing on a narrow set of core skills during the early years of education. Students are supported in the development of each skill to the point where they have mastered the concept. When, and only when, students have mastered each concept can they move on to the next skill.
Mathematics builds upon skills, you need to count before you start addition, you need multiplication to divide, you need division to master fractions, and so on and so forth. An approach which affords individual students the necessary time and practice to master each skill before moving on to more advanced operations, has clear benefits.
The development of students’ foundation in Mathematics is supported by carefully designed exercises which encourage students to identify patterns. Schools which follow the Mastery Method use a wide variety of visual representations to help the students make these connections. Number lines and fraction diagrams are also deployed by teachers to support students’ mastery of fundamental concepts.
Pretty much, everything can go with learning the four basic operations. Looking at the mastery method, it might be appealing to me. I even felt my hatred for Trigonometry dissolve when I found that it's part of life. However, higher mathematics is hardly taught with real-life examples. SOH-CAH-TOA doesn't make sense until more real-life examples are made. Just think if teachers talked about finding Trigonometry everywhere. Right now, I even find Calculus everywhere with every slope and curve in the road. However, classroom discussions tend to be forced to be boring.
Mastering every basic skill in mathematics is necessary for appreciation. It means not just memorizing formulas but their applications. Call me nuts but I believe mathematics exams also need essays, not just science exams. Students should spend less time with numbers but also understand why these formulas are needed. For example, I could now write an essay on Trigonometry. I could write about how Trigonometry starts with basic right angles but they help solve big problems. I would discuss how Trigonometry is used to measure house angles to ensure the right length is there. I could write an essay about Calculus and talk about how rates of change matter. Sadly, students aren't taught to do that. They can do SOH-CAH-TOA but need help to see its basic applications.
How rest periods may also be beneficial to mathematics learning
Not giving homework over the weekend may actually be beneficial not just to students but also to teachers. Back then, I survived it. However, after doing an exercise program, I want to stress that exercise rest days are vital. Academics is mental exercise and the brain needs to rest. Sometimes, I take a break by watching intellectually stimulating yet it's not required to be written as a report. I do blogging like this to ease my mind. I do set a schedule but the fact that I'm not being graded over my entries relieves the pressure.
I think about how Christmas breaks for students aren't really breaks. The only time students (and teachers) get to relax is on December 24 and December 25. However, on December 26, students are stressed out again. The same goes for the teachers. Teachers are required to start getting ready to check exams. The flight-or-fight response students will have is, "Sir/ma'am we have too much homework?" Unfortunately, teachers might be forced to say, "Shut up! You're not a student if you complain about homework over the holidays." I wonder if one of my former teachers left the teaching profession because she was forced by the school system to give homework over the holidays.
I mentioned earlier about exercise. I tried having exercise with no rest day. The result was that after 120 days of getting 8,000 steps--I hurt my back. The muscles are bruised and torn during exercise. Sure, exercise is needed but so is rest. All work and no play makes one stupid. Having at least one rest day from exercise can help the muscles grow back. The moment I took a break from exercise having five to six days of exercise was helpful. The next thing I knew I could walk for more than an hour without much pain in the legs.
The same concept can be done with schooling. Students should be given time to bond with their families, have time to rest over the weekend and the holidays, and the like. The students (and teachers) should have no extra work over the two weeks. Vacation during the Christmas break isn't going to be long. If machines need rest then so do humans. A computer or a calculator can blow up if it's overused. How much more the human mind will blow up from overwork. Maybe, it's time to distance exams a week or two weeks after the vacation. Make use of the next two weeks to build momentum. Maybe, the solution is to have more days of schooling so the third grading doesn't become hectic.
If students are well-rested, they can learn mathematics better. Some students catch up with mathematics faster than the hours. A well-rested mind is going to be more ready for mathematics. Mathematics is always going to be that hard gym exercise. A body that's not well-rested isn't ready to hit the gym. The mind that's not well-rested is sure to suffer in mathematics class.
Yes, we should never forget what history teaches us. A classmate of mine, back in high school, wrote a simple and blunt essay called "History: A Teacher". I doubt he still has a soft copy, given it was already more than 20 years ago. I'd like to quote Duterte critic Andrew James Masigan wrote this in Philippine Star --something that should remain relevant: I would never undervalue the 1987 Constitution. It dismantled the legal framework of a repressive regime and established the democratic institutions we enjoy today. For this, I am grateful. The 1987 Constitution was crafted with the best of intentions. It sought to put the Filipino first in all aspects of governance and to level the playing field amongst sectors and peoples. But it is far from perfect. It failed to consider the importance of foreign capital and technologies and the stiff competition we would have to face to obtain them. In short, its economic provisions were short-sighted . So despite the Constitut...
I would like to apologize in advance to my readers. The picture I'm presenting is in Tagalog, and not all my readers speak Tagalog. I would translate the picture's text into English for convenience. It says: "Ano ang bumubuo sa mga presyo?" means "What comprises the price?" "Gastos ng materyales" means materials expense "Gastos sa kasangkapan" means depreciation expense ""Gaston sa pasahod" means salary expense "Kapitalista" means capitalist Renta is well, rent "Kayang pababain ang presyo" means "Prices can be lowered". It says that capitalists (industrialists, landlords, bankers) and elitist governments are part in the gross profit. Get rid of excise taxes (either permanently or temporarily) for the prices of goods and services. In the times of crisis, in the burden of sacrifices, we need to be watchful for capacity. Whatever savings for times of difficulty by the workers and countrymen, the...
Chinoys of my age (and older) may remember these textbooks. I called them as the "symbol of trauma". It was memorizing something without understanding it . One would just memorize (without understanding it) because it was typical. Not being able to memorize what was assigned? Get a bad grade? One can expect physical punishment like hitting the hand with a ruler or chili in the mouth. Chinese language teachers are stereotypically strict . The language textbooks (above) are what were used during the 1990s to the early 2000s. As I wrote it, the Sinjiang textbooks aren't effective in teaching Mandarin , in a world where Mandarin has over a billion speakers! There's a Chinese proverb that says, "死記硬背 sǐ jì yìng bèi" or "Memorize to the point of death". That's exactly what those textbooks are. Memorize to the point of death! Okay, it may sound exaggerated. However, that's how Chinese language teachers in the Philippines were made to teach the ...
March 17 (which is tomorrow) seems to be an unofficial holiday for some people, right? I'm sickened that the late Flor Contemplacion has been treated like she's some national heroine (and thankfully, tomorrow isn't a holiday) even after Singapore had proven her guilt. A movie was made by Joel Lamangan called The Flor Contemplacion Story . The call for Migrante (Migrant) International has been to remember Flor even after several years. What's not too surprising was to learn that Flor's sons were all arrested for drug-related charges. Even her eldest son died while in prison. You have Migrante International wanting to end the labor export policy. However, a post by Migrante really shows how this group fails basic economics. I will not post the whole press statement but one part that made my eyes roll. >> Further opening the country’s economy to foreign ownership and control will worsen the exploitation of our people and the environment without creating a susta...
I guess nobody saw the Asian 21st Century coming, right? China was once a poor nation but look at it now. Vietnam was once a poor nation but look at it now. Singapore was once a poor nation but look at it now. The late great Lee Kuan Yew wrote his book From Third World to First . I'm afraid some people have been using it to go against the presidency of Ferdinand R. Marcos Jr. while ignoring what else Lee Kuan Yew had to say. Lee Kuan Yew described the Filipino press to be rambunctious on pages 304-305 which I agree. I'm afraid that the Filipino press may have had a hand in getting rid of any economic or political reforms that could help the Philippines. Yet, one policy has been holding back the Philippines for decades and yes, it's the Filipino First Policy . Reviewing the Filipino First Policy and why it has no place in the rising Asian 21st century I remembered how the values education subject taught Carlos P. Garcia's stupid Filipino First Policy as a Filipino value...
It's been some time since Jesse M. Robredo died too soon. Hopefully, his wife Atty. Maria Leonor Gerona-Robredo is true to her word, in her willingness to amend the 1987 Constitution of the Philippines, for the sake of foreign investments. It's a shame I never wrote about the late great man. The CoRRECT Movement on Facebook gave this important note on Robredo's life. Robredo said, "It's not enough for an official to be good. There has to be a system that forces them to be good." Whether or not Robredo was for charter change or a few constitutional amendments, I can't tell. For some racists, let me remind them that Robredo's real surname is Lim and his paternal grandfather is the late Lim Pay Co. In terms of Robredo's credentials (and I tend to sometimes brag about the credentials of those I quote), here's what the City Government of Naga website says: He is an Edward Mason Fellow and a graduate of Masters in Public Administration at the John...
Tomorrow is Bonifacio Day. It's effortless to say that Filipino First Policy works. I wouldn't be surprised if Andres Bonifacio gets used as a poster boy. However, Bonifacio worked for British and German investors . I'd like to talk about how decades of Filipino First Policy compromised our education system. Some idiot on Facebook said which I'll paraphrase to avoid getting personal. The idiot said, "If you let foreigners invest here, can Filipinos afford it?" The same idiot also scorns the law of supply and demand (read my post discussing why that's plain silly here ). People who believe in #SahodItaasPresyoIbaba must first prove it works by opening such stores nationwide, to show that the Philippines doesn't need FDI to succeed (read here ). Of course, I can expect them to say "It's the government's responsibility to raise salaries without raising the prices of goods." That's just plain bad accounting and finance too! Andrew Ja...
If there's any reason why some people are angry with the rich--it's because of rich people who look down on the poor. Some people are born rich without knowing the struggles of the one who originally acquired the wealth. Some rich parents make the fatal mistake of making their children feel entitled. Meanwhile, some rich parents make their children do the right thing by not waiting until things get too far. Some rich parents end up making their children attend middle-class schools, do summer jobs, work as employees in their own businesses, and teach them the value of wealth, especially by narrating the struggles before they got wealthy. In looking for a business partner, I feel it's very important to look at the attitude of these people. How do they treat people who do menial work? I could imagine looking forward to a business contract. However, it turns out that the potential business partner is a spoiled brat . Maybe, it's already a red alarm if I'm invited to an ...
I remember during the late 1990s when the song "Dayang Dayang" (Princess of the First Degree) was played on the radio. The origins are often debated whether or not it was from Muslim Mindanao or from the other neighboring countries. The Philippines has had settlers also from Malaysia and Indonesia. A parody cover by the late Yoyoy Villame was called Dayang Daya or Cheating Cheating. It was probably making fun of the Indian five-six lending business. Indians tend to be called Bombay because of the location known as Mumbai. I even made the mistake of referring to Indians as "Bombays" more than once. The song "Dayang Daya" does talk about the five-six lending services. It does target a lot of gullible people. I even became nearly distrustful of Indians in college for quite some time. I wrote how a Merry Christmas may lead to an Unhappy New Year due to debt burden (read here ). I tend to say to myself, "Somebody hasn't paid their debt!" every ti...
Monopoly - Hasbro I was looking at the CoRRECT Movement Moderated Public Forum on Facebook. I found more illogical arguments by a certain troll in the forum named Juan Dalisay Jr.--the writer of the Superphysics One website. However, this isn't the first argument I ran into as I've seen arguments from Kabataan Partylist and the League of Filipino Students on Facebook. They have claimed that foreign direct investments (FDIs) will lead to exploitation, only they will get rich, that they will rape resources, and an even funnier claim is that they will lead to monopolies . Some people, even fools, should be allowed to defend themselves at CoRRECT Moderated Public Forum than just live in their echo chamber of Facebook pages. However, Kishore Mahbubani and the late Lee Kuan Yew had long disproven that . The testimony is in the book From Third World to First by Lee himself. Mahbubani said foreign investors create jobs, bring capital, and teach new skills. I wonder if protectionist adv...
