This is my first English blog article. Probably there are some grammatical errors, and thanks for your patience.
Recently I am reading [A Mathematician's Lament], a discussion about problems of traditional k12 math education. I was touched. The fisrt half of the book helped organize and speak out what I doubted about my junior high school math.
Below is my story. Math was the worst subject I performed in my junior high school. The exams were usually about geometry. All I had to do was to add guidelines and prove a claim like "showing (angle) XXX is 45 degrees". Possible lines burst out of my mind, but not all of them would work, and I it was impossible to try all of them at school. Homework was a lot, and exam time was limited. Being afraid of my math teacher to announce “time is up”, I struggled with questions uncompleted. Junior high school geometry turned to be my anxiety.
"Which guidelines should be added here? And why?" The exams were like gambling. If I made a guess and failed to work it out, time lost. Gradually, I did not dare to walk out my first step for proof. And I was confused in class, that why the teacher added guidelines in a fixed way, and how did my classmates come up with the "standard" solution.
All the anxiety accumulated. In 2018, when the mock graduation test ended, I was afraid of my math teacher saying, "if you done this question wrong, stand up", and giving a criticism. I asked my mother to text the teacher that I would be absent the next day. She agreed, and the teacher permitted.
Nobody told me why making guidelines in a specific way. All I heard was "this is a xxx model, so add like that", but why? Until in 2020, my senior high school friend told me, "I came up with xxx because this dot (pointing at the center of the circle) looked strange". Well, it was not a perfect explination for me because I don't understand how to define "strange", but at least it was a reason.
Another nightmare was calculation. I made lots of calculations mistakes in high schools. My senior high school teacher was confused about that, but one thing he mentioned (when having discussion with my mother) was, "math is intuition". I did not fully understand that in 2021, but later I realized a little bit, which I will talk about later. And in my opinion, "intuition" also means math is not supposed to be a calculation tool.
In 2023, I met a nice professor teaching "Logic, Sets, and Proof" in college. I chose this class and found him treating math as an art and philosophy. While taking this course, I was reading [Logic: A Very Short Introduction], whose idea inspired me that proof is using a clear way to persuade others in a reasonable way. Or in another word, it's the ability to explain ideas.
My thoughts about mathematical proof may not be perfect, but I feel relieved. I remember at the first or second day of lectures, my professor was doing proof, writing "there exists ... such that" (in my opinion "such that" is similar as "which allows") and paused. I can't recall if he introduced the philosophy idea of existence, but "existence" was something that he emphasized. At that time, I made an idea connection. "Which came first: chicken or the egg" flew my mind, and suddenly I gasped. Proof is the representation of the world! It's a philosophy! Damm! (When I was writing this blog, this scene triggers my senior high school school mate, whose favorite slogan was (printed on the school advertisement), "existence precedes essence" by Jean-Paul Sartre. Probably it was not talking about math, but I am amazed by it.)
After that lecture, the word "intuition" wirls in my mind, but I cannot explain it clearly. Intuition of Domino (this was my math professor's explination about induction)? Or the intuition of solving a problem (the road between claim and conclusion)? Or the intuition of finding a road between the starting point and the destination？I am not sure(lol). But my confidence is gradually back.
I have finished my story telling, and let us go back to the book. My conclusion is, math is not just a tool, and it should not be recitation. For me, junior high school tests were not "math", as it discouraged students spend time to think about possible approaches and try their ideas. It is fine to fail with some roads, but like art, no one rules a fixed solution as long as other ways also work out. Though preciseness is important, before that, creativity is essential.
Today when my group wrote down "loves(x,y)", the professor talked with us. "We need to define 'loves'... （can't remember) We need to make sure it's x loves y, not reversible" (ahh, a sad story (lol)), he beamed, "It's quite Valentine's Day, right?"
(Written on Feb. 15, when I sent the email to math faculty about enrolling in the math minor. Unfortunately, I was not replied.)
Last modified on 2023-02-15