科学与数学j2kun.svbtle.com
数学家总是长期处于迷失和困惑之中
Mathematicians are chronically lost and confused
2014 — 2016，它一次次回到首页
黑点是上首页（≥ 50 分）的那次投稿，空心点是没冲上去的投稿，点越大分数越高。
导读
数学家 Jeremy Kun 撰文指出：即使是职业数学家，也长期处于迷失和困惑的状态——困惑不是失败的标志，而是学数学的常态。文章旨在打破“别人学数学都很轻松、只有我不行”的错觉，鼓励学习者接受这种不确定感。
为什么经久不衰：它戳中了无数人在数学学习中遭遇挫败感的共同经历，把“困惑”重新定义为学习过程的正常部分，因此多年来反复引发共鸣。
HN 评论精选
数学教育碎片化，学生从未被引导看到数学的整体图景
英国的中学数学教育只教初等代数、欧氏几何、简单微积分，矩阵、群论、数论这些要到大学才接触，甚至根本没人告诉你数学有哪些分支。每个阶段都在学零碎挑选的技能，只见树木不见森林，大多数人一辈子都不知道森林的存在。
nly查看英文原文
Secondary math education, for me in the UK, didn't deal with anything outside of elementary algebra, Euclidean geometry, some statistics, and relatively simple calculus. Nobody talked to us about imaginary or complex numbers, or bayes theorem, decision theory, or non-trivial mechanics problems until I was in college (age 16+). Nobody mentioned matrices, broader number theory or discrete transforms until I was in university. I studied EE not compsci. Things like algorithmic complexity I had to learn for myself and from Knuth. I'm trying to grok group theory right now to help with my understanding of crypto. Before this, it was never mentioned throughout my education, so I don't know what courses you would have had to take to learn that. The fact that I didn't even know group theory was important to crypto until after I had made the choice strikes me as a bad sign. The common theme at every level is learning cherry-picked skills, before you're even told what the branches of mathematics even are. Everything seems disjointed because you're not taught to look past the trees for the forest. Most people infact, even technical folk, go through their entire lives without knowing the forest even exists. Any idiot can point to a random part of their anatomy and posit that there's a field of study dedicated to it. The same goes for mechanics or computer science. You just can't do that with mathematics as a student. I loath academic papers. Often I find I spend days or weeks deciphering mathematics in compsci papers only to find the underlying concept is intuitive and plain, but you're forced to learn it bottom up, constructing the authors original genius from the cryptic scrawlings they left in their paper... and you realise a couple of block diagrams and a few short paragraphs could have made the process a lot less frustrating. So many ideas seem closed to mortals because of the nature of mathematics.
数学学习中的'断层'时刻摧毁自信，教学法应系统性地应对它
很多人学数学多年一帆风顺，直到遭遇第一次真正的断层——可能是乘法表、分数、几何证明或极限。反应几乎千篇一律：'我果然不擅长数学'，从此信心崩塌再也追不上。学校缺少应对这种断层的系统方法，其实我们可以帮学生准备好面对这种恐慌。
acjohnson55查看英文原文
I've felt this is the case for a long time. A lot of people have a smooth experience in math for years until they hit their first serious discontinuity. That could happen anywhere: times tables, fraction arithmetic, two-step equations, geometric proofs, radicals, limits, or maybe even college math. The reaction is nearly universal though. The person thinks, "holy crap, I guess I'm actually not good at math", anxiety strikes, and they freeze up. Some people find eventually find their way around this first road block, and future discontinuities in understanding become less stressful, and eventually understood to be a completely normal part the process. But the usual experience is that a person's math confidence is blown and as the math truck barrels on ahead, they never catch up. They understandably accept the identity of not being "good at math". What's missing in math pedagogy at most schools is a systematic way to deal with the discontinuities when they strike, especially that first time. We can prepare students to deal with that panic. The tough part is that the math teacher probably has 90 students on roster, but the discontinuity could hit pretty much any given lesson, for some given student. I know so many people who have come back to intermediate math later in life and breezed through it, armed with intellectual confidence gained from other fields. They look back and wonder how they came to be so intimidated by math in their younger days. We've got to give younger people the tools and knowledge for overcoming this intimidation at a younger age. We've got to kill "I'm just not good at math".
一线教师从这些讨论中汲取灵感，用数学故事保持学习的趣味
我教处于困境中的学生数学。这些讨论改变了我教学的方式：除了概念和技巧，我会时不时给孩子们讲数学故事——'有些无穷比另一些无穷更大'、'你的密码在 Facebook 上是怎么存的'、'高斯小时候一分钟算出 1 加到 100'。谢谢大家的分享。
japhyr查看英文原文
I currently teach math to at-risk students. I don't read all of these submissions about math education, but I skim the comments on most of them. The comments people make change the way I teach math. I have always done a decent job of teaching math. I focus on helping students understand concepts, even when they are focusing on mechanics. I use words like "shortcut" and "more efficient method" rather than "trick" when showing students more efficient ways to solve problems. I have students do problems and projects that relate to their post-high-school goals. But with the routines of school life, I get away from the fun of math from time to time. The comments on these submissions often remind me to go in and just tell stories about math: - "Hey everyone, did you know that some infinities are bigger than other infinities?" - "Hey everyone, do you have any idea how your passwords are actually stored on facebook/ twitter/ etc.?" - "Have any of you heard the story about the elementary teacher who got mad at their class, and told everyone to add up all the numbers from 1 to 100? One kid did it in less than a minute, do you want to see how he did it?" Thanks everyone, for sharing your perspective on your own math education, and about how you use math in your professional lives as well. Your stories help.
数学成熟度很难在正规教育之外获得，它深刻改变思维方式
这关乎'数学成熟度'。许多程序员重视能力和经验胜过正规教育，但数学恰恰是很难在正规教育之外自学的学科。系统的数学训练真的会改变思维方式，正是这种成熟度的缺失，让普通程序员转向科学计算比反过来更难。
laingc查看英文原文
To me, this is about "mathematical maturity". My observation is that many programmers, especially those who have come of age by working in startups, tend to value ability and sometimes experience over formal education. This is a result, I believe, of noticing that they can outperform many people who have a classical education, and also seeing that many of the people to whom they look up also do not have much in the way of formal education. However, I truly believe that Mathematics is a discipline that is very hard to engage with outside of formal education - or at least nobody has really found a great model for doing so yet. Learning Mathematics in a classical, structured way really does change the way you think. I notice a substantial difference even between those of my colleagues who entered industry straight after their Masters or even Bachelors, and those who completed Doctorates or even held postdoctoral positions. In my opinion, it is this lack of mathematical maturity that makes the switch from general programming to scientific programming more challenging than the converse.
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