Advice for teaching math to friends?
Question：
My high school has a knack for making math seem more complicated than it actually is (almost as if Lockhart’s Lament incarnated). I’ve learned that almost all of my classmates are having difficulty learning Trigonometry this year and even Algebra the past years. So, I often find myself teaching concepts to my friends since I’m apparently the mathematician/physicist of the group.
However, while I still find the topics simple and feel that I understand it well enough to teach, I sometimes find my students still confused, even if it was just visualizing concepts. I’ve always believed in Einstein’s quote saying “if you can’t explain it simply, you don’t understand it well enough,” but maybe I need something more. I want to spread the beauty of math just as everyone here has been doing!
I’ll take any advice you have. I’ve found that sometimes I end up cluttering my ideas, and I throw more words than I feel I should, so tips for organizing ideas would be helpful too!
这大概就是数学学霸的忧伤吧……
Answer:
我不知道题主所谓的“三角学”包括哪些部分，在中国，初中的三角学包括：
- 三角形
- 全等三角形
- 相似三角形
- 三角函数
- 勾股定理
- 圆和三角形、四边形和三角形
等等
I don’t know what the “Trigonometry” you mean. In China, trigonometry in junior middle school includes:
- Triangle
- Congruent triangle
- Similar triangle
- Trigonometric function
- Pythagorean theorem
- Circle and triangle, quadrilateral and triangle and so on.
确实，很多人都不能很好的理解有关三角形的知识，我一开始在学习的时候也感到吃力——尤其是三角函数。我的方法是：
- 把所有的概念画到图形上
- 多自己亲手画图
- 自己推导所有的公式、定理
It’s true that many students do not understand something about triangles well, and I am also struggling at the outset of learning - especially with trigonometric function .My approach is:
- Draw all concepts onto the figure
- Multiple oneself handedness sketchdrawing
- Derive all the formulas, theorem yourself
希望能帮到你！ Hope can help you!
The pandemic is beating the last bits of my love of math out from me, and I don’t know what to do.
Question：
It’s 12pm. I’m writing out the answers to some stupid exam with easy questions that no longer interest me. It’s been months since I last managed to read more than 5 pages from a maths book, or hell enjoy much things at all. (The only thing that sometimes keeps me entertained is bullet chess).
After years and years of being passionate about maths, and everything about it, from the education system teaching me that my love for not calculating things out is wrong, to being rejected by every higher-educational institution I actually wanted to go (both for BSc and Masters), it seems this is the final straw. The thrill I used to get after that last nice step in the proof is gone for me, and I don’t know what to do. My whole life was meant to be based around mathematics, but it feels like every time I take a step in that direction, the mathematical world pushes back against me.
I used to get very involved in projects. It seems every time I do, I am a burden to professors there, not someone they enjoy talking to about random interesting intricacies, the way I was. Meanwhile, all sorts of further study programs don’t seem to care about my clear passion, my grades, or anything, just choosing me to reject me with the standard “we are too busy to even bother giving feedback” (and oh, I have tried).
I’m not burnt out; I barely spend time doing maths as is anymore, I go on walks (which is my favourite escape) and socializing with friends fairly often. But I just feel so hopeless. For some reason, this stupid virus has really just absolutely destroyed everything of my mathematical mental state, with things such as “columns of matrices are vectors” no longer being the instant sharp thought they were, but instead coming beleaguered after minutes of staring at them.
Whatever am I to do? Has anyone else suffered from this? How did you escape it?
其实每个人都有这么一段路程——对于我们很喜欢的一件事物，突然对他失去了兴趣。怎么办？
Answer:
I can understand what you felt like. It must be a very bad because you can’t do something you like.
I still remember my experience when I was in Grade six. I did’t like math at all at that time because my first math teacher had to work in another school and the new teacher was an old man. I didn’t like him at all! Even though his was very funny, I couldn’t remember any words.
I told it to my father. He said that it was very normal for everyone. “Never give up anything if you really like it. Nothing can stop you working on this.”
I think it can help you. Maybe you don’t like some branches of math but you have to learn it, that’s okay. Nobody can just study one of them. As long as you still love math and brave enough to face any trouble, everything will work out.
The best wishes to you!
