正文翻譯

Why are math teachers so bad at explaining things?

為什么數(shù)學老師這么不擅長解釋?

評論翻譯

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義和消極的。他們都沒有考慮到數(shù)學作為一門學科的獨特性。這個問題的主要答案就是——數(shù)學確實是一門很難教的學科。
想想你在學習數(shù)學時的任何體會。有些問題看起來讓人望而生畏，但一旦你看到了答案，往往看起來應(yīng)該是顯而易見的。通常是因為存在一個非常優(yōu)雅的，也許是相當有創(chuàng)意的解決方案。
每當你看到“美麗的解決方案”并確信問題比實際更容易時，想想吧。事后看來，一切似乎都更容易。在教數(shù)學時也會發(fā)生類似的事情。你理解的數(shù)學越多，就越難衡量材料的難度?？破詹┲?blue1brown在他的一個視頻中很好地說明了這一點。
最后，他談到了數(shù)學教科書的作者，他必須提出實踐問題。他指出：
“在各種各樣的貢獻者中，有一點是不變的:沒有人能說出他們的練習有多難。知道數(shù)學什么時候難比數(shù)學本身更難?！?br>我認為這是作為一名教師和學生都應(yīng)該牢記的。

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：文化和管理實踐。
美國對數(shù)學既敬畏又鄙視。一方面，人們對黑板上長而復雜的方程印象深刻；另一方面，他們說“我在現(xiàn)實生活中要這個干什么？”這影響了許多數(shù)學教師的看法：其中一部分人希望給人留下深刻印象；另一部分則是尋找最簡單的方法——以犧牲功效為代價。
地區(qū)指導方針扼殺公立學校的K-12教育體系的教師；因此，即使是優(yōu)秀的人也會受到官僚主義的影響。最讓學生失望的是強制的教學方法。在大多數(shù)情況下，這是死記硬背。
在大學里，教授和學生一樣容易患上記憶疾病。更糟糕的是，他們經(jīng)常負責重申這一意識形態(tài)，并為學生成為教師的另一個周期加油。
死記硬背導致解釋力差。

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.

阿諛奉承的記憶者可以完成博士學位，他們正是這項任務(wù)的首選類型：他們很容易被塑造，以適應(yīng)組織中的每一個突發(fā)奇想。當他們成為教授并經(jīng)營公司時，他們的性格不會神奇地轉(zhuǎn)變。
數(shù)學教授在研究型大學工作是為了聲望，為了大量撰寫論文和獲得資金。這是一場給人留下深刻印象的表演，而不是教學。因此，他們會盡可能地削減教學方面的每一環(huán)節(jié)，當一切都失敗時，他們會很方便地指責學生。
這門課很難——所以更有理由準備好盡可能順利地解決難點
學生不讀課本”——如果教授不能條理清晰地回答問題，那么大量的教材閱讀對他們來說是有幫助的
數(shù)學系顯然忽視了高效、清晰的溝通技巧。幾個月來，我在一家校對公司工作，這家公司甚至為美國一流的大學提供服務(wù)，我遇到的大多數(shù)數(shù)學作業(yè)都很糟糕。實際上，我丟掉了那份工作，因為我不能在不重寫的情況下使上一篇論文達到標準，而且我的改進建議對教授來說“不夠?qū)捜荨?br>當我在大學當數(shù)學老師時，我對其他老師和教授的懶惰和冷漠感到非常失望。是的，有些學生不想動一根手指，但這種形象往往是錯誤的，尤其是教授。他們最小化了自己群體的缺陷，最大化了其他群體的缺陷。

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，我將拋出一個共同的問題。大多數(shù)大學預科數(shù)學是由對數(shù)學不特別感興趣或不擅長數(shù)學的人教授的。當然，也有很多例外，但數(shù)學是大學預科每一年的必修課程，而且沒有足夠的數(shù)學愛好者來教所有人。
想象一下，一個音樂老師對音樂沒有鑒賞力和天賦。他可以告訴學生如何握住樂器，如何發(fā)出不同的音符。他可以講授音樂風格、歷史和理論。所有這些東西都可以通過死記硬背來學習和傳授。但他無法解釋音樂的本質(zhì)或價值，也無法激勵學生，他們也無法進行令人愉快的表演。
雖然每個學科都有好老師和糟糕的老師，但比起欣賞數(shù)學的數(shù)學老師，更容易找到熱愛文學的英語老師、迷戀過去的歷史老師和對體育上癮的體育老師。

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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?

我讀了很多書，有些東西讓我難以釋懷，如果你能向一個8歲的孩子解釋，就說明你已經(jīng)完全理解。這些老師沒有一個能向一個8歲的孩子解釋，他們幾乎不能就他們自己找到答案的關(guān)鍵向一個大學生解釋。
為什么沒有人得出這樣的結(jié)論，這些老師只是不太懂微積分，為那些既擁有終身教職，又對我們的未來扮演法官、陪審團和劊子手角色的教授們想出一大堆借口。

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.

數(shù)學和物理老師總是受到學生的批評和憎恨，這就是問題所在。大多數(shù)學生從來沒有為了理解而學習，充其量他們只是為了即將到來的考試記住一堆垃圾。除非你真的在數(shù)學或物理課上學習并跟上進度，在課前閱讀相關(guān)章節(jié)，否則你從課堂上得到的東西很少，你完全無法理解。這不是教學法的缺陷，一般來說，這是在許多目標受眾中發(fā)現(xiàn)的缺陷。