Does the Grades-Over-Learning Approach Contribute to Students Hating Mathematics?

Schoolessons

Some time ago, I wrote about why I used to hate school. The big problem has to be that the education system cares more about grades than learning. A good grade is indeed a sign of good character. A good grade is only good if it is achieved without cheating. However, for a grade to be really good--I believe that it must spring out from learning. However, the education system has been so focused on grades over learning that students end up cheating as a result (read here). It affects every subject since a faulty system is a faulty school of thought. I'm going to really point out that I hated school because of the grades over learning approach. It's always all about grade shaming and even the best teachers end up indirectly or inadvertently participating in it. I still remember two of my best strictest teachers. One was as stern as the late Miriam Defensor Santiago. Another was the reason why I never dropped out.

This time, I'd like to focus again on mathematics. It's no secret that I really hated mathematics in high school. Since the education system cares more about grades than learning--mathematics is no exemption from the rule. Just think of how math classes can be. One reason why I'm naming trigonometry a lot is because I hated it a lot during high school. It didn't matter if the teacher was a very encouraging person. What mattered to me was, "When am I going to use this?" That's the question that every student has in every mathematics class. All branches of mathematics are part of life. The problem is how mathematics classes often fail to connect with life. I even feel stupider just thinking about how I never knew how trigonometry was applied until later in life.

I could remember an incident back when I was 11 years old. After I got the answer wrong, I simply shouted "I hate math! I hate math!" The teacher tried to comfort me and I told her, "Ma'am I give up! Just get over it! I'm stupid!" It didn't matter even if the other two teachers I had (and both migrated to the USA) tried to stop me. I was really the math-hating pessimist. The teacher tried to help me but I always felt that I was useless. I was garbage because I wasn't good at mathematics. I fell into despair and had suicidal thoughts all because of my math anxiety. In my fourth year of high school under K+10--I even wanted to quit because calculus and trigonometry felt so complicated.

Mathematics is not just something to study but to learn. One can spend the whole time memorizing formulas without knowing their applications. That was what mathematician Paul Lockart tried to emphasize. It's effortless for some people to brag about how often they ace mathematics exams. However, let them get into a practical mathematics exam and they might fail. One could brag how good they are at proving geometric and trigonometric identities. However, they can easily fall if asked, "How are these used?" They might end up making irrational answers if their course didn't use mathematics in that way. For all I know, a mathematics teacher may never know the simplest applications such as how architects use calculus to compute curves and the right amount of materials to use. They might not even know the everyday applications of any mathematics subjects. Their knowledge of mathematics focuses excessively on the theoretical side. Even worse, some boomers might protest against practical education because they weren't "taught that way". Then they wonder how their children (and even their grandchildren) may become bigger idiots than them (read why here).

This is my favorite excerpt of The Mathematician's Lament by Lockart. This is what the education system is failing at and why mathematics comprehension is that bad:

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.

Just think about it when mathematics is so grade-based--it's either you get it or you don't. I used to want to bash Trace Dominguez's videos on mathematics. However, looking at this video, I guess one can say why the whole "I'm not a math person." thinking persists like a pandemic. It's because people are taught just how to do math and not to understand math. Some people are better at mathematics than others. That's why some people can survive the very mathematics-intensive courses that require a lot of science. How can students understand mathematics if all they're doing is memorizing formulas without knowing how they're applied?

After reading the history of mathematics during the COVID-19 pandemic, I do feel the real problem is there. I did research on Chinese mathematics to the point I wrote an entry about it. One of the many things I mentioned from Domino Chinese:

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.

In short, I may actually be better at mathematics than I know. Building the fundamentals is necessary and the focus must be on learning. Memorizing the basic arithmetic table helps us navigate through life. Learning about fractions helps us through life. We must think about building the fundamentals than throwing everything at full velocity. The mastery method isn't just plain memorization but also the development of a solid foundation. When the focus is learning over grades--mathematics starts to become more interesting, Mathematics is only boring because it's almost comparable to getting the highest possible score in a Pac-Man game. How many people want to play that very old game today where you only focus on getting the highest score than learning? Instead, a more interesting computer game to play is if one can share their discoveries rather than their scores in the game. The same can go for how school goes.

Mathematics will be hated less when mastery is the focus. If mathematics teachers were encouraged to discuss applications as well. I used to get mad and wish that many people who "invented" mathematics were never born. One of the stupidest things to happen is that the history of mathematics is unknown until physics class. Shouldn't people learn about the history of mathematics as early as Grade 1? Shouldn't the history of every mathematics subject be introduced aside from focusing on equations? Shouldn't real-life applications be the focus?

I don't think grading will go away soon. Grades may still be used to assess pass or fail. However, if the focus was merely on pass or fail, there would be more failing grades in real-life assessments. We're often told that our grades will affect our future. An educator will one day see the student they had a problem with due to bad grades. The poor student can get better grades later in life. However, the problem is if grading is put on top of learning. Learning is compromised. People can get an excellent score but never know what they are studying, Many times, an excellent score can be bought by bribery. It's no wonder some people who care too much about honors would go to a school with a poor honesty track record. If I were a swindler, I'd get rich fast by having a school with a terrible honesty record. Parents who care too much about grades will want to enroll in my school rather than a school with a better honesty record. Schools with better honesty records may become concentration camps since the education system cares more about grades than learning.

Some people will overcome their hatred for mathematics. I overcame it later in life though I recall it a lot. I admit that I did get a failing mark in mathematics more than once. Wouldn't it be better if people started overcoming it much earlier? If the approach was all about learning mathematics than just merely getting a high score--there would be better scores in the long run. Give them a mathematics surprise test with practical questions--they may answer it well. Let them write an essay about how calculus is used--they may end up expounding it even if they may not be that articulate. This would also provide a constructive conversation between students, teachers, and parents.

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