尖子生是怎么学习的？ - 龙腾网移动版

Jessica Su
I am an above-average student at Caltech. I don't think I study particularly hard, but I do

我是加州理工学院的中上水平学生。我并不觉得自己特别努力学习，但我确实做到以下几点：

Get 8-9 hours of sleep a night. This allows me to go to class well-rested and do my problem sets with greater efficiency.

每晚睡8-9个小时。这让我能精神饱满地去上课，并且更高效地完成作业。

Always go to class. Even if the lectures are not useful, they serve to structure my day. Having lots of free time creates diminishing returns for me - three hours isn't too different from four hours, but having one block of three hours and one block of one hour is significantly better.

一定要去上课。即使有些讲座没什么用，但它们可以帮我安排好一天的时间。对我来说，空闲时间太多会导致效益递减——三小时和四小时的差别不大，但如果有一段三小时的时间和一段一小时的时间，就明显更好了。

Spend a lot of time working on my problem sets before I ask others for help. I like to think that all my time spent getting nowhere on problem sets gives me a deeper understanding of the material. And I don't know about you, but I find it way easier to concentrate when there's no one else in the room.

在向别人寻求帮助之前，我会花很多时间自己做作业。我觉得，即使在作业上花了很多时间没有什么进展，也会让我对材料有了更深的理解。我不知道你怎么想，但我发现，当房间里没有其他人时，我更容易集中注意力。

Start my sets the day they come out (at least for the first few weeks!). You'll probably spend more time on them, but being ahead will boost your morale. Plus you'll have time to go to office hours and you won't feel pressured to pull an all-nighter on the last day.

我在作业发布的当天就开始做（至少在前几周是这样！）。你可能会花更多的时间在作业上，但提前完成会提升你的士气。此外，你还会有时间去参加办公时间（教授或助教的答疑时间），这样你就不会在最后一天因为赶不完作业而感到压力大到熬夜了。

For some classes, I read the book before going to lecture. Try and have a schedule for reading the book so you don't slack off. Also, you won't have time to read the book for all your classes, so choose wisely.

对于某些课程，我在上课前会先读课本。试着为读书安排一个计划，这样你就不会懈怠。此外，你不可能有时间读完所有课程的书，所以要明智地选择。

Use the Mac app SelfControl to block Quora, Facebook, and other distractions during the day. I promise I'll turn it on after this answer!

使用 Mac 应用中的一个叫自我控制的APP来阻止你白天浏览 Quora、Facebook 和其他分心的内容。我保证在我答完这个问题之后就会开启这个APP！
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Oh, and for math classes, you really have to read the proofs. Don't be one of those students who skips over them because they have no relevance to the problem sets. Reading the proofs will build up your mathematical maturity, just like lifting weights builds your muscles.

哦，在数学课上，你确实需要阅读数学证明题。不要成为那些跳过数学证明的学生，因为他们觉得这些证明与作业无关。但实际上，阅读数学证明可以帮助你提高数学能力，就像举重可以增强肌肉一样。

David Koh
I did pretty well at MIT, and there's a few things that I did there that haven't been mentioned yet.

我在麻省理工学院（MIT）的表现相当不错，有一些我在那里做的事情还没有被提到过。

The most important thing is to keep track of how good your understanding is of the material. I saw a lot of people thought that they understood what was going on in a class, but could easily get tripped up by the basics even after the class had moved onto more advanced topics. Having a thorough understanding of the basics is particularly key, because most advanced material is really just an extension of the basics.

最重要的一点是要时刻掌握你对课程内容的理解程度。我见过很多人认为自己理解了课堂上的内容，但即使在课程进入更高阶的主题后，他们仍然很容易被基础知识绊倒。对基础知识的透彻理解尤为关键，因为大多数高阶内容实际上只是基础知识的延伸。

For most mathy, computer science topics, there's really two parts to understanding. The first is intuition, which for me always meant being able to build a mental model of whatever I was studying in my head. Usually, working out examples helps with the intuition. The second is knowing how to formally reason about the topic, which usually involves being able to work through examples step by step using logic and/or algebra, and is especially key for proofs in math and algorithms. Most good students learn the rules for formal manipulation fairly well, but without a good intuition it becomes harder to deal with more complex problems, where the correct path is not immediately clear.

对于大多数涉及数学或计算机科学的主题来说，理解实际上分为两部分。第一部分是直觉理解，这对我来说通常意味着能够在脑海中构建出所研究内容的心智模型。通常，通过解决例子有助于培养这种直觉。第二部分是知道如何正式地推理这个主题，这通常涉及通过逻辑和/或代数一步步地解决例子，对于数学证明和算法来说尤其重要。大多数优秀的学生能很好地掌握形式化操作的规则，但如果没有良好的直觉，在面对更复杂的问题时，正确的解题路径可能不会立即显现出来，这就变得更难处理。

Another important thing, especially at top schools, is time management. If one class just clicks for you and you get it easily, and another class is really hard, you should be able to spend less time on the first in order to spend more on the second. Good students study smart, not hard (great students usually do both).

另一个重要的事情，尤其是在顶尖学校，就是时间管理。如果一门课对你来说很容易，你能够轻松掌握，而另一门课却非常难，那么你应该能够在第一门课上花费较少的时间，以便在第二门课上花更多时间。优秀的学生会聪明地学习，而不是盲目努力（顶尖的学生通常两者都做到）。

Here's some tips broken down by part of the class:

以下是按课程部分分类的一些建议：

Lecture

讲座

I find that in lecture, one of three things happens for me: (1) Everything goes too fast and I get lost. (2) I can follow what the professor is doing and I understand what they're talking about. (3) The professor is going kind of slow, and I can usually get a good idea of where they're going before they say it.

在讲座中，我发现自己通常会遇到以下三种情况之一：
（1）一切进展得太快，我跟不上。
（2）我能够跟上教授的讲解，并理解他们在说什么。
（3）教授讲得比较慢，我通常在他们讲之前就已经大致明白他们要说的内容了。

In case (1), it usually means that I'm going to need to do extra work beforehand and afterwards in order to get anything out of lecture. This usually means doing the readings beforehand, and going over the lecture notes afterwards until I feel confident I know what the professor was talking about. Office hours and recitation are also great places to ask to have something explained again, and hopefully this time in a way you can understand.

在情况（1）中，通常意味着我需要在课前和课后额外做一些工作才能从讲座中获得收获。这通常包括课前阅读相关材料，以及课后复习讲座笔记，直到我对教授讲解的内容感到有把握。办公时间和辅导课也是很好的地方，可以请教教授或助教再次解释某些内容，希望这次能用一种你能理解的方式来讲解。

In case (2), I usually don't worry too much about doing readings beforehand, but I will go over the lecture notes, since usually there are some things I didn't realize I missed. The key thing to know here is that I never really feel like I understand the material yet at this stage, since I usually know the 'how' but not the 'why'. The 'why' typically comes with problem sets.

在情况（2）中，我通常不会太担心提前阅读材料，但会复习讲座笔记，因为通常会发现一些自己没注意到的遗漏。关键是，在这个阶段，我通常还不会完全理解材料，因为我通常知道了“怎么做”，但不清楚“为什么这样做”。“为什么”通常是在做作业时才会明白的。

In case (3), I may skim the lecture notes, but otherwise I'm usually good. Case (3) usually only happens when I've seen some of the material before anyway, so I usually have a pretty good idea of how well I know it.

在情况（3）中，我可能会快速浏览讲座笔记，但通常没什么问题。情况（3）通常发生在我之前已经见过一些材料的时候，所以我通常对自己掌握的程度有一个比较清晰的了解。
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One last tip that I think is really key for lecture is to try to understand how the professor thinks and where they're coming from. For instance, my math professor for Real Analysis always thought of the concepts he was teaching in terms of metaphors and visuals, and he would always start with that, and then tie it into the rigorous math. From that, I knew what the structure of the lecture would be and also that I would get good intuition from the professor (but he might leave out some of the rigor). In contrast, I had another professor in Probability who did everything through equations, which meant I got most of my intuition about topics from the book.

最后一个对讲座非常重要的建议是，尽量理解教授的思维方式和教学出发点。例如，我的实分析课程教授总是通过隐喻和视觉化的方式来解释概念，他会先用这些方法来引导我们，然后再深入到严谨的数学证明中。这让我能够了解讲座的整体结构，并从教授那里获得很好的直觉（但他可能会省略一些严格的数学细节）。而在我另一门概率课程中，教授主要通过方程式来讲解内容，这意味着我对这些主题的直觉大部分来自于课本。
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Problem Sets

习题集

Problem sets are usually the best place to find out how well you actually understand the material. Always start them alone, because if someone else gives you the key intuition for a problem right at the beginning, they've just prevented you from finding a hole in your own understanding you didn't know was there.

问题集通常是了解自己对教材理解程度的最佳途径。一定要单独开始做题，因为如果别人一开始就给了你问题的关键直觉，他们就会阻止你发现自己理解上的漏洞。

Here's how I typically do problem sets. First, read the whole thing, and then start on the easiest looking question. Work on it until you've either solved it, or you're stuck and not sure what to do next. Then move to the next easiest question, and so on, until you've tried all of them. Which questions you can do and can't do right off the bat are good indicators of how well you understand a certain topic.

我通常是这样做问题集的。首先，阅读全文，然后从看起来最简单的问题开始。直到你解决了这道题，或者你卡住了，不知道下一步该怎么做。然后再做下一道最简单的题，依此类推，直到把所有题目都做完。哪些问题你一开始就会做，哪些不会做，这些都是你对某个主题理解程度的良好指标。

Once you've done a first pass of the problem set, take a short break, and then double down again on the problems, one at a time. If you get really stuck on a problem, skip it again, but I'll usually only do this if I spend more than half an hour without getting anywhere. You may try lots of things and hit lots of dead ends while working on problems this way, but that is good, because you are learning what doesn't work, which is something you can't usually learn in lecture (and is very important on tests).

做完第一遍问题集后，休息片刻，然后再重新做题，一次做一道题。如果你真的在某个问题上卡住了，就再跳一遍，但我通常只在花了半个多小时却毫无进展的情况下才会这么做。用这种方法做题时，你可能会尝试很多方法，也可能会遇到很多死胡同，但这是好事，因为你可以学到哪些方法是行不通的，而这是你在课堂上通常学不到的（这在考试中非常重要）。
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Finally, once you've given all the problems a good, honest try, go and find help. Friends and classmates, TAs and professors are all good options. Hopefully, they can help you get unstuck on the problems you're still stuck on. At this point, you should be able to understand the solution they gave you, and if not, keep bugging them until you can.

最后，在你认真尝试解决所有问题后，去寻求帮助。朋友、同学、助教和教授都是很好的选择。希望他们能帮助你解决仍然卡住的问题。此时，你应该能够理解他们给你的解决方案，如果还不能理解，就继续问，直到你弄明白为止。
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Studying for Tests

考试复习

First thing I always did to get ready for a test: Find a practice exam, and do it cold, before you study at all, no notes or helpers. This will give you a very good idea of how well you know the material, and is likely to be an hour or two well spent. Make sure you skip things that haven't been covered yet, if the test is from an older version of the class. If you can't solve a problem, note that down and move on.

我准备考试时总是首先做的事情是：找一份练习考试，并在完全不参考任何笔记或帮助的情况下直接做一遍。这将给你一个非常好的了解，知道自己对材料掌握得如何，这通常是非常值得花一两个小时的。确保跳过那些尚未讲过的内容，如果练习考试是旧版本的。若遇到解决不了的问题，记下来并继续做其他部分。

Review the test and see what you didn't know. These are the things that are most important to study. The other key thing to do is see what topics weren't covered on the test, and make sure you study those as well. If you can find another test that did have a problem on that topic, I suggest doing that problem as well, to test your understanding.

复习考试并查看你不知道的内容。这些就是你最需要重点学习的内容。另一个关键是查看测试中没有涉及的主题，确保你也学习这些内容。如果你能找到另一个包含这些主题问题的测试，我建议你做这些问题，以检验你的理解。

Another good technique is to make a list of all the topics on the test, and see how much the class has covered those topics. This gives you a good idea of how hard the problems on those topics will be. If you've had a lot of problems or lectures on a topic, the test will probably have more advanced problems about it, but probably fewer. Conversely, if you've only covered a topic a couple times, the test will probably give you easier problems, but there might be more of them. This is just a rule of thumb and is sometimes completely off, but it is often helpful to guide studying.

另一个好方法是列出测试中所有的主题，并查看课堂上已经覆盖了多少这些主题。这可以给你一个很好的了解，知道这些主题上的问题会有多难。如果你在某个主题上做了很多题目或听了很多讲座，考试中可能会有更高级的问题，但数量可能较少。相反，如果你只覆盖了某个主题几次，考试中可能会给你更简单的问题，但可能会有更多。这只是一个经验法则，有时可能完全不适用，但通常对指导学习很有帮助。

Non-trivial problems - I consider test problems that require an extra insight which was not necessarily taught in class to be a special class of problems. There's not one good way to prepare for them, since you don't really know what's coming, but having a really solid intuition of the basics is usually really helpful. Also, a good understanding of general related topics can be invaluable, which means just being a good all around student will probably help you on the hardest tests.

对于非平凡的问题——我将那些需要额外见解而课堂上没有明确教授的问题视为特殊类型的问题。没有一种好的准备方法，因为你不知道会遇到什么，但对基础知识有非常扎实的直觉通常很有帮助。此外，对相关一般主题的良好理解也可能非常宝贵，这意味着，成为一个全面优秀的学生可能会帮助你在最难的考试中取得好成绩。

Help other people study! Explaining concepts you think you understand is a great way to find out where the gaps in your knowledge are. If you don't know anyone who needs help with the class, find someone who already knows the material and "teach" it to them. They will be able to tell you what you didn't talk about, or things that you got wrong, and they may be able to ask questions you don't know the answers to (and then answer them for you)

帮助别人学习！解释你认为自己理解的概念是发现知识盲点的好方法。如果你不知道有谁需要帮助，找一个已经掌握了这些材料的人，并“教”他们。这样，他们可以告诉你你没有提到的内容，或你讲错的地方，他们可能会提出你不知道答案的问题（并为你解答）。

Taking Tests

考试技巧

You can probably find tons of test taking tips elsewhere, so I'll stick to the basics here. Read the whole test beforehand, start with the easiest problems first, followed by the ones that are worth the most points (if you know how much they're worth).
If you get stuck on a problem, make sure you show work up to where you are, and go to a different one. Partial credit on everything is good.

你可以在其他地方找到很多考试技巧，所以我这里只讲一些基本的要点。首先通读整份试卷，然后从最简单的问题开始答，接着做那些分值最高的问题（如果你知道它们的分值的话）。如果你在某个问题上卡住了，确保展示你已经完成的步骤，然后转到其他问题。部分得分是很有帮助的。

If you get stuck on a non-trivial problem which is really hard (and you're done with everything else), trying something that you're not sure if it works usually doesn't hurt, and sometimes the professor might give you partial credit if you were kind of close. If it feels good to your intuition but you can't justify it formally, you're probably not far off.

如果你在一个非常难的问题上卡住了（且其他问题都做完了），尝试一些你不确定是否有效的方法通常不会有坏处，有时教授可能会因为你接近正确答案而给予部分得分。如果这个方法在直觉上感觉不错，但你不能正式证明它，那么你可能离正确答案不远了。

Finally, one last note: If you feel like you're starting to get overwhelmed by a class, don't lose hope! Go back to the basics, and learn them again. If the class is moving too fast for you, you have to go back, put in the time to learn it at your own speed, and build up your understanding piece by piece. Often, advanced concepts are built up one simple step at a time from the basic concepts, and if you missed some of the steps in the middle, it's easy to feel like nothing makes any sense anymore.

最后一点：如果你感觉自己开始被课程压得喘不过气来，不要失去希望！回到基础，再次学习这些基础知识。如果课程进度对你来说太快，你需要回到前面，以自己的速度花时间学习，并一点一点地建立理解。通常，先进的概念是从基础概念逐步建立起来的，如果你在中间遗漏了一些步骤，很容易觉得一切都没有意义了。

Rob McQueen
I've been at MIT for the past four years in course 6 (Computer Science), and I'm currently studying for my last final exam (!!!). Here are some things that work for me:

在过去的四年里，我一直在麻省理工学院攻读第六课程（计算机科学），目前正在复习最后一次期末考试（！！！）。以下是一些对我有用的方法：

Teach it first: To understand new systems / concepts, stand up in front of a chalkboard and act as if you're teaching it to a class. When you get to a point you don't know how to explain, talk it out. Literally, stand up and talk to yourself; it works.

先试着教它：为了理解新的系统或概念，站在黑板前，假装自己在给一班学生讲课。当你遇到一个不知道如何解释的点时，把它说出来。真的，站起来对自己说，这很有效。

Diagram / Symbol: Once you understand something, create a visual diagram / symbol. Draw it on a piece of paper. Close your eyes and think about it in your head. Once you have the diagram / symbol, it will be very easy to remember how it works later on.

图表/符号：一旦你理解了什么，就创建一个可视化图表/符号。把它画在纸上。闭上眼睛，在脑海中思考。一旦有了图表/符号，以后就很容易记住它是如何工作的。

Believe everything is easy and simple: You might not understand certain systems at first look, but if you approach it with a simple mind, you will do better. You won't think too much about the details and you will better understand the high-level picture.

相信一切都很容易和简单：乍一看，你可能无法理解某些系统，但如果你以简单的心态对待它，你就会做得更好。你不会过多地考虑细节，而会更好地理解全局。

Sleep on it: Read a paper before you go to sleep and think about it as you doze off. When you wake up, it will be at least 50% easier to understand.

睡前思考：睡前读一篇论文，边打瞌睡边思考。当你醒来时，理解起来至少会容易 50%。
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Make sure you get enough sleep: It makes it incredibly easier to understand new systems when you are thinking clearly. If you're studying and things just aren't making sense, take a nap for 20 minutes. It may be just enough to get the lightbulb in your head to flicker.

确保睡眠充足：当你思维清晰时，理解新系统会变得无比容易。如果你在学习中遇到不明白的地方，可以小睡 20 分钟。这也许足以让你脑中的灯泡闪烁一下。

Discuss it with friends: Discussions help you gain new perspectives on how others think of systems. It might introduce variables you never thought about.

与朋友讨论：讨论有助于你从新的角度了解他人是如何看待系统的。它可能会引入你从未想过的变量。

Marc Milgrom
I barely survived engineering at Cornell, but I did get better at it. I can tell you some things NOT to do, and what I've since learned better. Much of this comes from the Coursera course "Learning How to Learn," and its companion book, A Mind for Numbers, both of which I highly recommend.

在康奈尔大学攻读工程学时，我勉强活了下来，但我确实学得更好了。我可以告诉你一些不应该做的事情，以及我后来学得更好的东西。其中大部分内容来自 Coursera 课程《学会如何学习》及其配套书籍《数字思维》，我强烈推荐这两本书。

Get enough sleep-- your brain simply doesn't crystallize new information and function properly with insufficient sleep

充足的睡眠--睡眠不足时，大脑根本无法形成新的信息并正常运转

Don't cram: brain patterns form from spaced repetition of material and from practice, and it's very hard to learn and retain material all at once; computer science and other technical fields like science, engineering and math are inherently cumulative so retention of prior concepts to build new ones is necessary

不要填鸭式学习：大脑模式是通过有间隔地重复材料和练习形成的，很难一次性学习并保留所有材料；计算机科学以及科学、工程学和数学等其他技术领域本身就是累积性的，因此有必要保留先前的概念以构建新概念

Practice: the only way to get better at coding (I assume that's why you're in CS?) is to keep doing it and look at other people's code only after you've made attempts to solve problems yourself; likewise for math and engineering problems; just reviewing and understanding solutions creates what's called the "illusion of competence"

实践：提高编码水平的唯一途径（我想这也是你学习计算机科学的原因吧？）是不断实践，在尝试自己解决问题之后再看别人的代码；同样，数学和工程问题也是如此；仅仅回顾和理解解决方案会造成所谓的 “能力错觉”。

In terms of studying, read the end of chapter summaries, notes, and problems first as a guide for what you'll be learning; this acts as a scaffold on which to hang the concepts as you learn them; at the end of a chapter, close the book and write down what you remember, then compare with the chapter summary

在学习方面，首先阅读章末摘要、注释和问题，作为学习内容的指南；这可以作为学习概念的支架；在一章结束时，合上书，写下你所记住的内容，然后与本章摘要进行比较。

Work steadily in periods of 25-30 minutes (Pomodoro method) and then break for 5 minutes then perhaps move on to a related topic or other subject; your brain will keep processing the prior one in the background.

稳定地工作 25-30 分钟（Pomodoro 法），然后休息 5 分钟，接着可能会转向相关主题或其他主题；你的大脑会在后台继续处理前一个主题。
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Work and study in groups where allowed and appropriate, but a) come prepared to contribute and interact, b) only work with people you can actually WORK with, and leave if the sessions are dominated by goofing off (hard, I know), and c) work with people of varying skills and strengths who can both teach and learn from each other. You'll learn more from explaining your thinking to someone else than studying on your own.

在允许和适当的情况下，分组工作和学习，但 a) 准备好贡献和互动；b) 只与你能真正一起工作的人一起工作，如果会议以打闹为主，就离开（很难，我知道）；c) 与不同技能和特长的人一起工作，他们既能相互传授知识，也能相互学习。与自学相比，向别人解释自己的想法会让你学到更多。
原创翻译：龙腾网 https://www.ltaaa.cn 转载请注明出处

Ben Leong
I was a decent student back when I was an MIT undergrad and now that I'm a prof, and I really want my students to do well. Every semester, I email them a lix to the following article by Cal

我在麻省理工学院读本科时是个不错的学生，现在我是一名教授，我非常希望我的学生们能取得好成绩。每学期，我都会给他们发邮件，让他们链接下面这篇文章，作者是 Cal
链接：

Newport: http://calnewport.com/blog/2007/10/03/the-art-of-stealth-studying-how-to-earn-a-40-with-only-10-hours-of-work/, which pretty much summarizes everything in about a thousand words.
If you don't have time to read the article, the hypothesis is that your brain absorbs information best in small chunks, so the key simply is CONSISTENCY.

如果你没有时间阅读这篇文章，那么它的假设是，你的大脑吸收信息的最佳方式是小块吸收，因此关键在于连贯性。

Learn topics that you are taught as soon as they are introduced in class and learn them well in small chunks. Do your problem sets diligently and put effort into understanding the material. Math requires practice if you want to solve questions consistently under exam conditions. How much practice you need will depend on your level of maturity (in Math).

课堂上一有课题，就立即学习，并分块学好。勤做题集，努力理解教材。如果想在考试条件下稳定地解题，数学需要练习。你需要多少练习取决于你的成熟程度（数学）。

Do not count on last minute cramming right before exams to do well. Cramming might work (i.e. get you decent grades in the exams) during the first two years when the material is relatively simple, but if you don't learn the basics well, you might end up having trouble with the more advanced material that will build on the basics. It might be hard to catch up once you have a gap in your understanding in the early years.

不要指望在考试前的最后一刻补习就能取得好成绩。在教材相对简单的前两年，填鸭式学习可能会奏效（即在考试中取得不错的成绩），但如果基础知识学得不好，在学习建立在基础知识之上的高级教材时可能会遇到困难。一旦在早年的学习中出现理解上的偏差，可能就很难迎头赶上了。