# 为什么数学老师这么不擅长解释(二)

Why are math teachers so bad at explaining things?译文简介

网友：我是一名数学老师，这个问题也让我困惑。然而，我对此有一些想法。1： 知道如何教数学和教数学所需的技能不同于知道如何做数学和知道如何理解数学。2： 试试这个练习：在键盘上输入你的名字。现在闭上眼睛，试着描述你在哪里找到了每个字母......

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Why are math teachers so bad at explaining things?

为什么数学老师这么不擅长解释?

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I’m a math teacher, and this is a question which puzzles me too.

I’ve some thoughts on it however.

1: Knowing how to teach math, and the skills required to teach math are different from knowing how to do math, and knowing how to understand math.

2: Try this exercise: type your name on a keyboard. Now close your eyes, and try and describe where you found each of the letters.

When you get really good at math, some of it is a bit like that, you no longer have conscious understanding of just what you did, so it becomes harder to explian it.

3: When you are really good at math, it becomes very hard to see what part of a problem is going to give difficulties.

我是一名数学老师，这个问题也让我困惑。

然而，我对此有一些想法。

1： 知道如何教数学和教数学所需的技能不同于知道如何做数学和知道如何理解数学。

2： 试试这个练习：在键盘上输入你的名字。现在闭上眼睛，试着描述你在哪里找到了每个字母。

当你非常擅长数学的时候，有些就有点像这样，你不再有意识地理解你做了什么，所以它变得很难解释。

3： 当你真正擅长数学时，很难看出问题的哪一部分会给你带来困难。

I believe that being a bad school teacher is the result of a double whammy.

1.) Teachers are NOT necessarily educated in the discipline that they are assigned to teach. I knew a teacher who was assigned to teach French, but he had no idea how to speak the language. My own sister-in-law can’t name the planets, but she was asked to teach science.

2.) Teachers are not really taught HOW to teach.

There is another thing that affects a teacher’s ability to teach well: Their neurological “wiring”—namely, the lateralization of our brain into two differently functioning hemispheres. A person who is "left-brained" is said to be more logical, analytical, and obxtive. A person who is "right-brained" is said to be more intuitive, thoughtful, and subjective. My opinion, as a teacher, is that the personality traits of a right-brained person are better suited to meet the unique demands of classroom teaching.

A left-brained teacher is more likely to be a disciplinarian who is less sensitive to the needs of each student. Whereas a right-brained teacher is more likely to appreciate the needs of each student and try to meet their needs and learning style.

In plain English: A left-brain teacher is the kind I had to endure most of my time in school. They are cold, uncaring disciplinarians (full of rules) and you don’t mess with them.

Fortunately, I had ONE right-brained teacher in grade 6, Miss Keagan, who really WANTED me to succeed. In a short time, she had me hooked. My midterm report card was amazing and she had the principal of the school present it to me in front of all my classmates. I was so proud. Of course, this was just another thoughtful way Miss Keagan used to entrench my confidence and joy of learning. This wonderful teacher is WHY I became a teacher. My only regret is that I never got to thank her before she died.

我认为做一个糟糕的学校老师是双重打击的结果。

1、老师们不一定接受过他们所教授学科的教育。我认识一位老师，他被派去教法语，但他根本不会说法语。我的嫂子叫不出行星的名字，但有人请她教科学。。

2、教师并没有真正学会如何教学。

还有另一件事会影响教师的教学能力：他们的神经系统“线路“，也就是说，我们大脑的两个半球，其功能不同。“左脑”据说更有逻辑性、分析性和客观性。“右脑”据说更直觉、更深思熟虑、更主观。作为一名教师，我认为擅长右脑人的人格特征更适合于满足课堂教学的独特要求。

擅长左脑的老师更有可能是一个对每个学生的需求不太敏感的严肃的人。而擅长右脑教师更可能理解每个学生的需求，并努力满足他们的需求和学习风格。

简单地说：擅长左脑老师是我在学校里大部分时间都不得不忍受的那种人。他们是冷酷的，冷漠严肃（充满了规则），你不会惹他们。

幸运的是，我六年级有一位擅长右脑的老师，Keagan小姐，她真的希望我成功。很快，她就让我爱上学习。我的期中成绩单非常棒，她让学校的校长在我所有同学面前把它给了我。我很自豪。当然，这只是Keagan小姐用来巩固我的信心和学习乐趣的另一种深思熟虑的方式。这位出色的老师是我成为老师的原因。我唯一的遗憾是在她死前我从未感谢过她。

False premise. Some are very good at explaining things, some are not. It gets difficult to uate when you consider that two students may be in the same class, with one believing that the teacher is great at explaining things, while the other believes that the teacher is not. We all don’t learn the same.

Generally, the more versatile a teacher is, and the better he or she can determine how to teach his or her students, the “better” that teacher is considered. Teaching is like any other profession. A few are really good, a few are really bad, and there are many “in the middle” somewhere. I suspect, but can’t prove that it’s close to a “normal distribution.”

这是一个错误的前提。有些人很善于解释事情，有些人则不然。当你考虑到两个学生可能在同一个班时，就很难进行评估了。我们都学不到同样的东西。

一般来说，教师越是多才多艺，他或她越能决定如何教学生，这个老师就被认为是“好”的。有一些真的很好，有一些真的很差，还有许多“处于中间”的状态。我怀疑，但无法证明它接近"正态分布"状态。

There are a number of answers here suggesting various reasons why it might be that math teachers do a less than stellar job. There’s probably some truth to some of those answers.

I, however, would suggest a completely different take: instead of focusing on teachers, recognize that students are often bad at learning math because they expect it to be explained to them, instead of working hard to understand it themselves.

Math is a skill. To develop a skill, you need to practice. The funny thing is that this is a completely obvious notion in most other endeavors that require skill. How often do people complain that piano teachers or football coaches are bad at explaining things? Would you expect to be able to build a chair or run a marathon after someone “explained it” to you? I’m sure you wouldn’t.

这里有许多答案表明，数学教师的工作不太出色的原因有很多。其中一些答案可能有些道理。

然而我将提出一个完全不同的观点：与其专注于教师，不如认识到学生往往不擅长学习数学，因为他们希望别人向他们解释，而不是自己努力理解。

数学是一种技能。要发展一项技能，你需要练习。有趣的是，这是一个非常明显的概念，在大多数其他需要技巧的努力中。有多少人抱怨钢琴老师或足球教练不善于解释？在有人向你“解释”之后，你会希望能造一把椅子或跑马拉松吗？我相信你不会的。

In short, you shouldn’t think of teaching as the act of someone putting knowledge into your head, but rather as someone helping you on your journey to learn. A great computer-science professor I had in college once said “stare at it until the pain goes away” when talking about some rather abstract definition. Teachers can show you the path and help you if you get stuck, but they can’t shove the information into your head, Matrix-style.

发展一项技能需要练习。学习数学需要练习。教师可以也应该以适当的难度向学生解释。但如果这些学生没有这样做，他们就会开始思考这个解释，试着在头脑中(或在纸上)重现它;；如果他们不接受所教的内容，并尝试将其应用到练习中，当他们陷入困境时，提出问题；如果他们不做这些事情，他们就不会学习。但这并不一定意味着老师不好，这需要双方的努力才能让教学发挥作用。我的猜测是，许多“数学老师不善于解释事情”的案例实际上是学生几乎没有做任何工作，然后抱怨他们的老师没有教他们数学。

简言之，你不应该把教学看作是一个人将知识灌输到你的头脑中的行为，而将其看作是一个帮助你学习的人。我在大学时的一位伟大的计算机科学教授在谈到一些相当抽象的定义时曾说过“盯着它看，直到疼痛消失”。如果你陷入困境，老师可以给你指路并帮助你，但他们不能像矩阵式那样把信息塞进你的头脑。

There are teachers who are good at explaining and others that are bad at it. Say 50% good, 50% bad.

As well, there are students good at learning and those bad at it. Say 50% good, 50% bad.

So if we assume that effective learning involves both good teaching and good learning, then only 25% of cases wil result in a positive outcome. And only 25% of students will feel they have been well taught.

Of course, this is very simplistic. In lower school most of the teachers aren't maths specialists, and maths is a specialist subject that involves concepts. And this further complicates the issue.

有些老师擅长解释，有些则不擅长。一半好，一半糟糕。

同样，也有擅长学习的学生和不擅长学习的。一半好，一半糟糕。

因此，如果我们假设有效的学习包括良好的教学和良好的学习，那么只有25%的案例会产生积极的结果。只有25%的学生会觉得自己受到了良好的教育。

当然，这是非常简单的。在初中，大多数教师不是数学专家，数学是一门涉及概念的专业学科。这使问题进一步复杂化。

Good maths teachers aren't. Good mathematicians often are though. I was taught by two very good mathematicians - good enough to have well-known equations named after them. One was at school, another at university. They were by far the worst of all the teachers I had. My theory is that people who find maths easy to understand are often bad at explaining it to people who don't.

好的数学老师不是。不过，好的数学家通常是这样。我的老师是两位非常优秀的数学家——他们优秀到可以用他们的名字来命名著名的方程式。一个在学校，另一个在大学。他们是我所有老师中最糟糕的。我的理论是，认为数学容易理解的人往往不善于向不懂的人解释。

Most graduates in mathematics have at some point struggled with a topic. Even those who did very well can’t remember how to solve problems and demonstrate to the freshman intake.

Mathematics is the only subject up to undergrad course where you can pass an example by doing exam type questions until anything that ever comes up has already been done before. Of course when the subject has only been taught to your year and the teach fails to provide a vast number of sample questions you may understand the work and may be able to solve the questions but not in the examination time allowed.

Some of those who are good at mathematics and become teachers never had a problem. Never had to work their way around or find another route to solving it. If they are also teacher training in mathematics they would be shown multiple ways to address that. Given 30 pupils in a class and 40 minutes to cover a 60 minute set of material there is little scope to demonstrate alternative ways that might suit a pupil better.

Even if you are usually good and had a good teacher you still might find somethings a struggle. Don’t expect to turn up to be taught. You go in to learn. The teacher is their to guide you, to pace the work and recognise what you know and how to use that to guide your forward. A class of 15 and that task is a joy. A class of 30 that might be impossible.

大多数数学专业的毕业生都曾在某个问题上挣扎过。即使那些表现很好的学生也不记得如何解决问题并向新生展示。

数学是本科课程中唯一一门你可以通过做考试题来通过例题的学科，直到之前出现的题都已经做过了。当然，当这门学科只学一年，老师不能提供大量的样题时，你可能会理解它，也可能能够解决问题，但不能在考试允许的时间解决它。

一些擅长数学并成为教师的人从来没有遇到过问题。永远不必绕道而行或找到另一条解决问题的途径。如果他们也接受数学方面的教师培训，他们会看到解决这个问题的多种方法。考虑到一个班级有30名学生，而60分钟的一堂课程有40分钟的时间学习时间，几乎没有机会展示可能更适合学生的替代方法。

即使你平时表现很好，有一个好老师，你仍然会发现有些事情很难。别指望去学校接受教育，你要主动去学习。老师是向导而已：指导你的进度，识别你的知识，以及如何利用这些知识来引导你前进。一个15人的班级，这个任务是一种乐趣，但是一个30人的班级可能是不可能的。

Often times it is more true that most students don’t have and they never had the right approach for learning math. They were always learning math as if it was biology or history and now the chickens are coming home to roost. To be fair it is not their fault. Somebody should have told them that the point of math is in understanding why formulas and techniques work, knowing how to construct proofs, being able to creatively use the knowledge that you have, being able to apply your knowledge and skill to solve problems etc. It is not about memorizing things.

Math, physics, computer programming are all about how well you can apply what you know. Theoretical knowledge means nothing if you can't apply it.

很多时候，更真实的情况是，大多数学生没有，他们从未有过学习数学的正确方法。他们总是把数学当作生物或历史来学习，现在却落得个恶果。公平地说，这不是他们的错。有人应该告诉他们，数学的意义在于理解公式和技术的工作原理，知道如何构造证明，能够创造性地使用你所拥有的知识，能够运用你的知识和技能解决问题等等，这不是记忆。

数学、物理、计算机编程都是关于你如何应用你所知道的。如果你不能应用理论知识，理论知识就毫无意义。

My mother was a math teachers. She made straight-A’s in school and only made one B while at University, the rest being A’s. Her two children understood math naturally with one becoming an accountant and the other an engineer. I’d believe she never understood how anyone could not be good at math and not understand it. Should she have picked a different career? Sure. But in her day and her area of the country, smart women became nurses or teachers. And a woman like my mother was never going to empty anyone’s bedpan. So teaching was her only real choice.

我母亲是一名数学教师。她在学校取得了全A，在大学只取得了一个B，其余都是A。她的两个孩子天生就懂数学，一个成为会计，另一个成为工程师。我相信她从来都不明白为什么有人不擅长数学却不理解它。她应该选择不同的职业吗？当然但在她那个时代和她所在地区，聪明的女性成为了护士或教师。像我母亲这样的女人永远不会清空任何人的便盆。所以教书是她唯一真正的选择。

I’ve tried to teach and tutor math and it is a very difficult thing to do. Two things make it especially hard: (1) there is an agreed upon result you’re trying to guide the student to and (2) there is no way beforehand to know what a particular student might respond to. There might be twenty or thirty ways to get any particular concept across, say how to calculate the area of a triangle. You try one, see how many respond by the glint in their eyes. Say half the class. That might leave another dozen people without a clue. So you try another. Then another. After half an hour of trying there may still be a couple of stragglers. Eventually you run out of time as you need to go onto the next concept. If the course was meant to cover twenty topics there may be as many as three quarters or more of your class that remained clueless on at least one topic. So they come to the conclusion that you’re bad at explaining things. One-on-one instruction is the only thing that I have found that helps.

我试着教和辅导数学，这是一件非常困难的事情。有两件事让它变得特别困难：（1）你试图引导学生达成一致的结果，（2）事先没有办法知道某个学生可能会做出什么反应。可能有二十或三十种方法来理解任何特定的概念，比如如何计算三角形的面积。你试其中一个方法，看看有多少人通过眼睛的闪烁做出反应，全班一半的学生说会，另外十几个人则毫无头绪。所以你试试另一个方法，然后是另一个方法。经过半个小时的尝试，可能仍有一些人不明白。最终，你需要讲述下一个概念，但时间就用完了。如果本课程旨在涵盖20个主题，那么可能有多达四分之三或更多的学生对至少一个主题上仍然一无所知。所以他们得出结论，你不善于解释事情。一对一的指导是我发现的唯一有用的东西。

I am strongly tempted to say that maths teachers are bad at explaining things , because they are used to dealing with numbers and not people! LOL.

Seriously, it really comes down to teacher training. As a School’s Inspector checking upon the quality of teaching in the whole range of school curricula, I have come across poor teaching in just about every subject (as did all my colleagues). Teacher training is a prerequisite qualification for teaching in schools. In teacher training, if you are specialising in a curriculum area, you are taught the most effective ways of teaching your subject specialism. (The trainee teachers in these instances all have considerable subject knowledge having a university degree in the subject.) During my own post-graduate training as a teacher, I specialised in teaching Biology and Chemistry to exam certificate level and general science in the first two years of secondary schools.

Even with teacher training, a teacher is expected to learn from experience i.e. reflect upon the effectiveness of what they have been teaching. This includes the cohort of students and the background from which they are drawn.

我很想说数学老师不善于解释事物，因为他们习惯于处理数字而不是人！大声笑。

说真的，这真的可以归结为教师培训。作为学校的督学，负责检查学校所有课程的教学质量，我几乎在每一门课上都遇到过糟糕的教学(我所有的同事也是如此)。教师培训是在学校任教的先决条件。在教师培训中，如果你专门从事某一课程领域，你将获得最有效的学科专业教学方法。（在这些情况下，受训教师都具有相当丰富的学科知识，并拥有该学科的大学学位。）在我自己的教师研究生培训期间，我在中学前两年专门从事生物和化学教学，以考试证书水平和科学概论。

即使是教师培训，教师也应从经验中学习，即反思他们所教内容的有效性。这包括学生群体和他们的背景。

The art of teaching lies first in capturing the attention of the students (i.e. making the subject relevant to them and their world) and then breaking down the task of teaching the ‘topic’ into manageable sizes and in ways that the student can understand.

Whenever I found that students were not picking up on a science concept - say osmosis for instance, I would try a different approach.

我记得在格拉斯哥（苏格兰）一个非常贫困的地区教科学概论（给13岁的孩子）。这些学生中的许多人被认为是哑巴或没有学习能力。大约45年后，我仍然记得的一次事件。一个学生在我的书桌上捡起一个重金属物体。他用手称了称，估计了它的重量。他接着告诉我每磅（重量）铜的价格。不一会儿，他告诉我，如果我把这件东西卖给当地的废金属代理商，它能卖多少钱！那堂课的大多数学生都能告诉你所有关于博彩公司的奇数以及比如说，当赔率是X时，在一匹马上下注1英镑，一个人可以赢多少钱。那对我来说是完全陌生的领域，尽管我有数学方面的资历!

教学的艺术首先在于吸引学生的注意力（也就是说，让主题与他们和他们的世界相关），然后将“主题”的教学任务分解成学生可以理解的范围和方式。

每当我发现学生们没有学会一个科学概念，比如说渗透法，我就会尝试一种不同的方法。

I recently wrote an answer where I said that both poetry and calculus can be useless to learn depending on the person learning them.

I got dozens of comments “Calculus clearly isn’t useless— look at all of these mathematical and real-world applications!”

I responded with the polite version of “Yeah, but I’m not doing the math, so why the hell should I care?”

That’s part of the issue with math teachers giving real-world applications for what they teach. There aren’t always real-world applications which students will care about.

If you ask your math teacher “When will we ever use this?” and they say “Well, mathematicians use this equation to do this, which in turn allows them to predict X, Y, and Z! That’s hugely important, because then it does QRS and LMN, which is what runs your computers/holds up your bridges/some other important function of society.”

我最近写了一个答案，我说诗歌和微积分都可能是无用的，这取决于学习它们的人。

我收到了很多评论：“微积分显然不是无用的——看看所有这些数学和现实世界的应用！”

我礼貌地回答道：“是的，但我没有学数学，所以我为什么要在乎呢？”

这就是数学老师把他们教的东西应用到现实世界的问题之一。学生们并不总是关心真实世界的应用。

如果你问你的数学老师“我们什么时候会用到这个?”他们说:“数学家用这个方程来做这件事，这反过来让他们可以预测X、Y和Z!”这是非常重要的，因为接下来它将执行QRS和LMN，这将运行你的计算机/支撑你的桥梁/社会的其他一些重要功能。”

You can’t reach everybody. Most kids will never see real-world uses for the specific equations and math concepts that they learn.

I assume it’s also an issue of time. Why waste the time explaining the uses of a concept when most of the class really doesn’t care? Especially with how cramped most teachers’ schedules are— it’s not a good use of their already-limited class time.

The skills you gain from learning math are always applicable no matter the field you go into, but the actual formulas and functions? Not so much.

数学老师试图教授任何给定数学概念在现实世界中的适用性是浪费时间的，因为许多孩子不涉足数学相关领域，而那些涉足数学领域的孩子可能永远不会再使用这个概念。

你不可能联系到每个人。大多数孩子永远不会看到他们所学的特定方程式和数学概念在现实世界中的应用。

我想这也是时间问题。为什么要浪费时间解释一个概念的用法，而班上大多数人都不在乎呢？特别是由于大多数老师的课表都被安排得很紧，这对他们本来就有限的上课时间没有什么好处。

无论你从事哪一个领域，你从数学学习中获得的技能都是适用的，但实际的公式和函数呢？没那么多。

Not all math teachers are bad at explaining things, but many are. It is because , usually, math came easy to them and that’s why they majored in math. The same is true for music teachers.

不是所有的数学老师都不擅长解释，但很多老师都不擅长。这是因为，通常情况下，数学对他们来说很容易，这就是为什么他们主修数学。音乐老师也是如此。