【龙腾网】为什么数学老师这么不擅长解释

正文翻译

Why are math teachers so bad at explaining things?

为什么数学老师这么不擅长解释?

评论翻译

Nico Lindsay
Some of these other answers are laughably egotistical and negative. None of them consider the uniqueness of mathematics as a discipline. The primary answer to this question is just that – that mathematics is genuinely a hard subject to teach.
Think about any realization you’ve had while studying math. Some problems seem daunting, but once you’ve had a look at the answer often times it seems like it should’ve been obvious. Usually because there exists a nicely elegant and perhaps rather creative solution being presented.
Think about every time you’ve seen that “beautiful solution” and convinced yourself the problem is easier than it actually is. Well duh, everything seems easier in hindsight. A similar thing happens when teaching math. The more mathematics you understand, the harder it is to gauge how difficult the material is. 3Blue1Brown makes a good point of this in his one video
by the end he’s talking about the author of math textbooks who must come up with practice problems. He noted that:
“Across a wide variety of contributors there is one constant: Nobody is able to tell how difficult their exercises are. Knowing when math is hard is waaayyyy harder than the math itself.”
And I think this is something to keep in mind both as an instructor and as a student.

其他一些答案都是可笑的自我主义和消极的。他们都没有考虑到数学作为一门学科的独特性。这个问题的主要答案就是——数学确实是一门很难教的学科。
想想你在学习数学时的任何体会。有些问题看起来让人望而生畏，但一旦你看到了答案，往往看起来应该是显而易见的。通常是因为存在一个非常优雅的，也许是相当有创意的解决方案。
每当你看到“美丽的解决方案”并确信问题比实际更容易时，想想吧。事后看来，一切似乎都更容易。在教数学时也会发生类似的事情。你理解的数学越多，就越难衡量材料的难度。科普博主3blue1brown在他的一个视频中很好地说明了这一点。
最后，他谈到了数学教科书的作者，他必须提出实践问题。他指出：
“在各种各样的贡献者中，有一点是不变的:没有人能说出他们的练习有多难。知道数学什么时候难比数学本身更难。”
我认为这是作为一名教师和学生都应该牢记的。

Joseph M.
Quick answer: culture and administrative practices.
America has both awe and disdain for mathematics. On one hand, people are impressed by long, complicated-looking equations on blackboards; on the other, they say “What the hell am I gonna need this for in real life?” This influences the outlook of many math teachers: one subset will look to impress; another will look for the easiest way out—both at the expense of efficacy.
District guidelines strangle K-12 teachers in public schools; so, even the ones who are good are compromised by bureaucracy. Whatever passes the most students is the enforced teaching methodology. In most cases, that’s memorization.
In college, professors are just as susceptible to the memorization disease as their students. To make it worse, they’re often responsible for reaffirming that ideology and oiling the gears for another cycle when their students become instructors.
Memorization leads to poor explanation.

快速回答：文化和管理实践。
美国对数学既敬畏又鄙视。一方面，人们对黑板上长而复杂的方程印象深刻；另一方面，他们说“我在现实生活中要这个干什么？”这影响了许多数学教师的看法：其中一部分人希望给人留下深刻印象；另一部分则是寻找最简单的方法——以牺牲功效为代价。
地区指导方针扼杀公立学校的K-12教育体系的教师；因此，即使是优秀的人也会受到官僚主义的影响。最让学生失望的是强制的教学方法。在大多数情况下，这是死记硬背。
在大学里，教授和学生一样容易患上记忆疾病。更糟糕的是，他们经常负责重申这一意识形态，并为学生成为教师的另一个周期加油。
死记硬背导致解释力差。

Sycophantic memorizers can complete doctoral degrees, and they are precisely the types preferred for the task: they’re easily molded to fit the department’s every whim. Their personalities don’t magically turn when they’re the professors and running the operation.
Math professors work at research universities for the prestige, for churning out papers and securing funding. It’s a show to impress, not to teach. As such, they’ll cut every pedagogical corner they can, conveniently blaming their students when it all goes down.
“The course is hard”—All the more reason to prepare to address the points of difficulty as smoothly as possible.
“Students don’t read the textbook”—A lot of good reading the textbook will do them if the professor is incapable of answering questions coherently.
Efficient, clear communication skills are apparently neglected in math departments. For several months, I worked for a proofreading company that services even top-ranking colleges in the United States, and most of the mathematics submissions I encountered were atrocious. I actually lost that job because I could not bring the last paper up to standard without rewriting it, and my suggestions for improvement “weren’t indulgent enough” for the professor.
When I was a math instructor in college, I was sorely disappointed at how lazy and apathetic many of the other instructors and professors were. Yes, there are students who don’t want to lift a finger, but too often this image is wrongly assumed, especially by professors. They’re minimizing the flaws of their in-group and maximizing the flaws of an out-group.

阿谀奉承的记忆者可以完成博士学位，他们正是这项任务的首选类型：他们很容易被塑造，以适应组织中的每一个突发奇想。当他们成为教授并经营公司时，他们的性格不会神奇地转变。
数学教授在研究型大学工作是为了声望，为了大量撰写论文和获得资金。这是一场给人留下深刻印象的表演，而不是教学。因此，他们会尽可能地削减教学方面的每一环节，当一切都失败时，他们会很方便地指责学生。
这门课很难——所以更有理由准备好尽可能顺利地解决难点
学生不读课本”——如果教授不能条理清晰地回答问题，那么大量的教材阅读对他们来说是有帮助的
数学系显然忽视了高效、清晰的沟通技巧。几个月来，我在一家校对公司工作，这家公司甚至为美国一流的大学提供服务，我遇到的大多数数学作业都很糟糕。实际上，我丢掉了那份工作，因为我不能在不重写的情况下使上一篇论文达到标准，而且我的改进建议对教授来说“不够宽容”
当我在大学当数学老师时，我对其他老师和教授的懒惰和冷漠感到非常失望。是的，有些学生不想动一根手指，但这种形象往往是错误的，尤其是教授。他们最小化了自己群体的缺陷，最大化了其他群体的缺陷。

Aaron Brown
Without agreeing with your premise, I will throw out one common issue. Most pre-college math is taught by people who are not particularly interested in or good at math. There are many exceptions, of course, but math is a requirement in every year of pre-college schooling, and there aren’t enough math-lovers who want the jobs to teach them all.
Imagine a music teacher with no appreciation and talent for music. He could tell students how to hold their instruments and how to produce different notes. He could lecture on musical styles, history and theory. All these things can be learned and taught by rote. But he couldn’t explain the nature or value of music, nor would he be likely to inspire students nor extract enjoyable performances from them.
While there are good and bad teachers in every subject, it’s easier to find English teachers who love literature, history teachers who are fascinated by the past and gym teachers addicted to sports—than math teachers who appreciate math.

在不同意你的前提下，我将抛出一个共同的问题。大多数大学预科数学是由对数学不特别感兴趣或不擅长数学的人教授的。当然，也有很多例外，但数学是大学预科每一年的必修课程，而且没有足够的数学爱好者来教所有人。
想象一下，一个音乐老师对音乐没有鉴赏力和天赋。他可以告诉学生如何握住乐器，如何发出不同的音符。他可以讲授音乐风格、历史和理论。所有这些东西都可以通过死记硬背来学习和传授。但他无法解释音乐的本质或价值，也无法激励学生，他们也无法进行令人愉快的表演。
虽然每个学科都有好老师和糟糕的老师，但比起欣赏数学的数学老师，更容易找到热爱文学的英语老师、迷恋过去的历史老师和对体育上瘾的体育老师。

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当你开始着手一个新项目时，通常需要建立一个全新的基础架构。这个耗时的过程可能需要设置多个工具，这些工具都需要集成和维护。使用不同的工具通常会造成贮仓，导致沟通不畅、协作效率低下和信息丢失。
借助JetBrains Space（一体化的完整协作平台），一个单一的、集成的开箱即用解决方案，你可以更快地完成这项工作，使你能够快速响应业务需求。
JetBrains Space是一个涵盖整个软件开发流程的统一平台，包括托管Git存储库、自动化CI/CD、发布软件包、协调云开发环境以及管理问题、文档和聊天——所有这些都在一个地方。
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IWISHTOLVE
I read a lot, and something stuck with me. . . If you can explain it to an 8 year old, you understand it PERFECTLY. None of these teachers can explain it to an 8 year old , they can barely explain it to a college student and they all have access to answer keys.
Why hasn’t anyone come to the conclusion that these teachers just don’t understand calculus very well, and come up with a bevvy of excuses for the professors who have both tenure and play judge jury and executioner with our futures?

我读了很多书，有些东西让我难以释怀，如果你能向一个8岁的孩子解释，就说明你已经完全理解。这些老师没有一个能向一个8岁的孩子解释，他们几乎不能就他们自己找到答案的关键向一个大学生解释。
为什么没有人得出这样的结论，这些老师只是不太懂微积分，为那些既拥有终身教职，又对我们的未来扮演法官、陪审团和刽子手角色的教授们想出一大堆借口。

Rory Coker
Math and physics teachers always get a lot of criticism and hate from students. Here is what’s at issue. Most students never learn how to study with the aim of understanding, at best they just memorize a bunch of garbage for the upcoming test. Unless you genuinely study and keep up in a math or physics class, reading the relevant chapter BEFORE the lecture, you will get very little out of the lecture… it will go right over your head. This is not a defect of the lecture, in general, it is a defect found in much of the intended audience.

数学和物理老师总是受到学生的批评和憎恨，这就是问题所在。大多数学生从来没有为了理解而学习，充其量他们只是为了即将到来的考试记住一堆垃圾。除非你真的在数学或物理课上学习并跟上进度，在课前阅读相关章节，否则你从课堂上得到的东西很少，你完全无法理解。这不是教学法的缺陷，一般来说，这是在许多目标受众中发现的缺陷。