Let's Learn the Practical Chinese Method of Mathematics Education

BBC

I could remember that when I was in my fourth year of high school (under K+10)--I frequently threw tantrums in Math class. I felt Trigonometry was the "most useless" mathematics. I always viewed myself as inadequate and unworthy all because I was labeled "bad at math". I felt I wasn't worthy because of that ,especially when I once aimed to enter the Ateneo De Manila University (ADMU) and get that "invincibility badge". I looked at some of my previous entries where I felt Chinese math was redundant since students are learning math in their English classes. Maybe, I'm wrong to say that. I decided to Google "Chinese mathematics" and I felt, "Maybe, it's time to apply the Chinese method of teaching mathematics in the English class instead!" I think Mandarin teachers should just focus on teaching 華語 (Huáyǔ) so students can speak better Chinese. 

I looked at Chinese mathematics. I heard some people who managed to reach the fourth year in Chinese (under K+10) say that Chinese mathematics has better reasoning than the regular mathematics class. I looked at the Domino Chinese website. I found this article by Daniel Maxwell, which shows the four reasons why the Chinese method of mathematics may actually be better than what we're all used to.

Reason 1: The focus on a growth mindset over a fixed mindset with mathematics

As mentioned earlier, I had a hostile relationship with most mathematics teachers, whether the teacher was benevolent (like the teacher who experienced my tantrums to the max) or it was that annoying elementary mathematics teacher. There's this mentality that people are fixed to certain talents and can't improve. Well, I can't say that's true because a former foe turned friend of mine wasn't good at composing essays. Yet, he did manage to improve himself over time after high school. Another former foe turned friend of mine was later cited, "He's not good in English but he doesn't get zero. He's trying to get better." I also find myself more able to understand maths and its applications in high school. I always had that fixed mindset. Sure, there are limits to growth but I'm proud to say that I did improve in mathematics to a certain extent. 

East Asian teachers, and parents, adhere to a belief that all children can obtain a proficient level of mathematics mastery, which creates a growth mindset. This belief in the ability of all students, plays an important part in teaching, learning and academic outcomes.

“All children are assumed to be capable of understanding, and ideas are elaborated in different ways in order to encourage individual understanding.”

Tim Oates

To understand what a growth mindset means, we need to understand the growth mindset at a surface. The Harvard Business Review presents this case of what it means to have a growth mindset:

Scholars are deeply gratified when their ideas catch on. And they are even more gratified when their ideas make a difference — improving motivation, innovation, or productivity, for example. But popularity has a price: People sometimes distort ideas and therefore fail to reap their benefits. This has started to happen with my research on “growth” versus “fixed” mindsets among individuals and within organizations.

To briefly sum up the findings: Individuals who believe their talents can be developed (through hard work, good strategies, and input from others) have a growth mindset. They tend to achieve more than those with a more fixed mindset (those who believe their talents are innate gifts). This is because they worry less about looking smart and put more energy into learning. When entire companies embrace a growth mindset, their employees report feeling far more empowered and committed; they also receive greater organizational support for collaboration and innovation. In contrast, people at primarily fixed-mindset companies report more cheating and deception among employees, presumably to gain an advantage in the talent race.

One of the biggest issues with mathematics class is often shame. True, not all teachers are monsters like the one I passed through for the first four years of my elementary life. However, there's always this mindset that gets implemented into, "I'm stupid in math! I'll never get better!" One of my most bitter memories was that I almost failed Grade 5 because of mathematics. I felt that being given a tutor meant I was stupid, therefore, I needed a tutor. There's the never-ending comparison between students left and right. It's always a huge problem, especially among those whose descent from Chinese immigrants was less than four or five generations.

What I'm thinking is that failure is not always final. It's one thing to fail in the exams. It's another thing when terror math teachers shame the student for getting the answer wrong instead of explaining it. In my case, even when the teacher tried to explain what went wrong, I told her, "Mam! Just accept that I'm stupid!" I guess that's been the mindset inculcated for a long time. Most of the time, the mathematics curriculum is based on a fixed mindset.

The objective of mathematics isn't to look smart but to be smart. It's possible to look stupid, and seem stupid, but to be very smart, and the other way around. Putting more energy into learning is to focus on how to get math right rather than being right all the time in mathematics. 

Reason 2: Confucian Ethics in Mathematics

One of the reasons Chinese Filipino schools tend to excel in Math might be Confucian ethics. Some people celebrate Teacher's Day on September 28 rather than October 5. Being Chinese by blood, I prefer to stick to September 28. 

A growth mindset towards Mathematics is further reinforced by other cultural factors. Chinese families continue to culturally adhere to Confucian ethics which highly value education, personal development and diligence.These cultural factors encourage and support students to take education seriously and work hard to do their best in school.

“A hard work ethic and a strong belief in the value of education is displayed by all families and instilled in every child” and it is these “attitudes and beliefs East Asian parents instill in their children make an important contribution to their high levels of academic achievement”.

John Jerrim 

Sure, Chinese parenting isn't perfect, and it needs to be modified every now and then. Again, who says that culture is static? The emphasis on education, personal development, and diligence doesn't need to come across negative Chinese stereotypes. A Chinese mother can choose to be a loving tiger mother (reasonably strict) or an unreasonable tiger mother (running things like Communist China). Atty. Amy Lynn Chua-Rubenfeld wrote the book The Battle Hymn of the Tiger Mother. There was that time when she found a more balanced approach with her second daughter, Louisa Chua Rubenfeld. Strict parenting is good only when it's got reasonable boundaries. I was able to read that book while I pursued my MBA at the University of San Carlos.

The issue I can raise with mathematics is the approach to learning. Was it just for the grades or for the learning? Personal development is often missed when it comes to coping with failure. Are the good grades gained from personal development and diligence? A good grade can be a sign of good character if it is achieved through personal development and diligence. A rise from a bad grade to a good grade through personal development. Some of the best rules would be limited screen time (because it's bad for the brain), exercise, never administering chores as punishment but necessity, respect for menial work, and focus on learning over prestige. It's because not everyone can become an honor student but anybody can gain what I call genuinely good grades. Good grades aren't necessarily excellent grades but grades that come from an emphasis on learning instead of just a grade. 

Cheating also happens a lot because the education system cares more about grades than learning (read here). Sure, we can't get rid of grading but it's not the end of it all. I was glad that teachers did try to help me when I was failing. I had several strict Chinese language teachers. My last two were known to be the strictest. In the end, they both asked me after I graduated college, "Was it true we were strict?" I answered, "Yes but I did learn something." However, their strictness wasn't so effective because the system didn't care too much about learning. 

Just think if mathematics was more focused on educating, developing the personality, and diligence instead of just winning content. I remember how we used to have a disciplinarian as strict as the late Miriam Defensor-Santiago. I remember how our students lost the math competition. She may have been known to be rather rash. However, she simply accepted the defeat. Meanwhile, I heard a certain mad woman shame the students in public for losing. One viewed the math quiz bowl's loss as an opportunity to learn. The other simply viewed it to stroke her arrogance. 

Reason 3: It's not just memorizing but also learning

There's the misconception that memorization is the end of it all. One of the biggest mistakes that people (and some Chinese Filipino parents of the older generation) made was to focus too much on memorization. Instead, this is an interesting piece of information that would be the difference between Chinese mathematics vs. the typical math class.

It’s often stated that teachers in China teach by rote-learning, and Chinese students are good at Mathematics, because they repeat calculations exercises over and over again. However, repetition does not help students master the fundamental concepts of mathematics nor prepare them to use Mathematics in real-life situations outside of the classroom. 

European educators who visited Chinese schools to observe Mathematics lessons noted that lessons were varied and engaging. Furthermore there was ample student-teacher interaction and student-student discussion rather than the ‘chalk and talk’  approach typically expected in Chinese schools. 

I'd like to say that "chalk and talk" is needed but not the end of it all. The issue that I had with most classes was that teachers were forced to use it, thinking it was better. I'd like to say my MDS-style teacher's brilliance and sternness were wasted by a bad system. Sure, we need to learn the basic formulas in mathematics. However, either we can talk too much about the formulas or let the students participate all the more. This also means that while repetition does occur, having more ample student-teacher interaction can help people who suffer from either math anxiety (like myself) or those who suffer from dyscalculia (who may consider taking special education) can help people

I'd like to go back again to trigonometry since I used to hate it with a passion. A person can brag all the want they memorized several trigonometric properties. One can start with the three basic functions of SOH-CAH-TOA. However, learning about trigonometry without learning how to use it in basic situations is a real problem. 

I never saw trigonometry this way in high school. I only viewed it as something to get rid of the classroom setting because "it was useless". I often had a quarrel with people who were better at math, hating them for simply being better. I even looked at their help as "looking down at me". I would even mockingly say, "So easy for you to say because you're better at math! Just give up because I'll never get it!" I had this hatred for mathematics like there was no tomorrow. My high school teacher would often ask how I was and if I still hated mathematics. Sure, she was a nice teacher but I still looked at mathematics as some "useless exercise". However, if mathematics were taught with more practical life applications and more student-teacher interaction, there would be better learning for mathematics. 

Reason 4: Focusing on mastering the subject instead of memorizing without mastery

Mathematics is an essential life skill. Sure, not everyone will be using trigonometry or engineering calculus. However, learning these skills will start to teach people the value of patience, and scientific method, and appreciate the things around them. I don't think I could really fully appreciate the buildings everywhere I go if I didn't study trigonometry and basic calculus in high school. However, I never saw it that way in high school and it's just because of teenager immaturity. I'd blame the lousy curriculum that defeats a good teacher most of the time. 

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. 

With mathematics, it's more than just drilling but also understanding. This video from DNews makes some sense after I read about the Chinese method of teaching mathematics. Unfortunately, students may have been given justification to be lazy because of the way mathematics is taught. It makes people lose interest. Trace Dominguez of DNews may want to cite Chinese methods in mathematics to back up his study. Yes, we can learn mathematics and we want to really focus on better methods. 

This video can explain what really is happening. People care more about their grades than their learning. Dominguez further reveals the problem of plug-and-chug mathematics instead of having a conversation. In short, teaching just how to do math but not to understand it isn't really an education. Paul Lockart reveals this problem with how math is typically taught:

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. 

I'll admit in my quest to get rid of high school mathematics (under K+10)--I soon realized that the problem is how teachers are made to teach mathematics. I had that crazy desire to go back in time and prevent famous mathematicians from being born. However, I soon found out how these mathematics are used. I found how these "useless maths" made the stuff I'm enjoying, such as the PC that I'm using to type this entry. Computer science is math-intensive to deliver the best accurate results. Engineering is math-intensive. It's because one wrong computation means it can create a domino effect. 

With real understanding, one can say that mathematics is not dull. Mathematics only seems dull because of the problem of too much memorization. In the quest to master the subject, a system that values creativity in delivering the facts, in showing the applications of lessons in daily life, and when learning arouses learning, the same goes for mathematics. 

Final words

My proposal is to integrate the Chinese method of teaching math into English math instead. Chinese schools may want to focus on the Chinese language subject. You don't need a mastery of Mandarin (or any Chinese dialect) to implement Chinese methods of teaching. It's learning how the Chinese schools do their mathematics and put them into a different language. We didn't need to learn Greek to learn mathematics. We didn't need to learn Greek to memorize formulas. Chinese method of mathematics education can be taught in any language.