练习解决问题技巧的最好方法是什么（二）

Dushka Zapata
How to develop problem solving skills:
First, I recognize my ego is always in the way. No, Dushka. This is not about you. You don’t have to save the day.
Make mistakes. Setting my ego aside also allows me to try different things without worrying that they might not work.
Ask why. Ask why again, and again. This brings the real problem into focus. (I am broke. Why? Because I buy things I don’t need. Why? Because I want them. Why? Because they make me feel I am in control in an uncertain world. Oh. I don’t need to “curb my spending” as much as I need to address my anxiety.)
Beginner’s mind. Look at the problem as if it was new, rather than looking at it as if only I can fix it.
Observe, and listen. This is the only way I can grasp the problem in its entirety.
Defy “root cause” logic. Is it possible that this problem has more than one root cause?
See the problem as separate from my experience solving problems. My experience shapes what I see, which can make solutions invisible. (To a hammer, every problem is a nail.)
Break down the problem into smaller problems that can be more easily solved.
Recruit people who are not like me.
Sleep on it. Never underestimate the power of taking a break from the problem.

如何培养解决问题的技能：
首先，我认识到我的自我总是在阻碍我。不，杜什卡(Dushka ),这与你无关。你不需要拯救世界。
犯错误:把自我放在一边,也让我可以尝试不同的事情，而不用担心它们可能不起作用。
问为什么:一次又一次地问为什么,这使真正的问题成为焦点。（我破产了:为什么？因为我买了我不需要的东西。为什么买？我想要它们。为什么想要？它们让我觉得在一个不确定的世界里，我可以控制自己。噢，我不需要像解决焦虑一样“控制支出”）
初心：将问题视为新问题，而不是将其视为只有我才能解决。
观察，倾听：这是我能全面把握问题的唯一方法。
无视“根本原因”逻辑：这个问题有可能有不止一个根本原因吗？
把这个问题与我解决问题的经验分开来看。我的经验塑造了我所看到的，这可以让解决方案变得不可见（对锤子来说，每个问题都是钉子。）
将问题分解为更容易解决的小问题。
招募与我不同的人。
把问题留在第二天解决：永远不要低估在（解决）问题中休息的力量。

Rohan Jain
"What can I do? This is not possible to solve."
When I was interning at BCG many years back, I was once faced with a problem that I found impossible to solve. After spending a few days on the problem, I gave up.
"I do not think this problem can be solved," I told my immediate superior. And guess what? I was blasted left, right and center.
"Had the problem been easy, wouldn't the client have solved it themselves? Do you think the client has hired us to tell them that we cannot solve the problem?"
I closed my laptop, took out a pen and notebook, and started trying to solve the problem again, but this time with a fresh approach. It did not work fully, but I felt I was a little bit closer to solving the problem. I kept pushing and eventually managed to arrive at an answer.
I learned my lesson - there is no problem that is impossible to solve. It might require resources, it might require expertise, it might require hustle.
But you know what? When not being able to solve a problem is not even an option, every problem can be solved.
If you want to get better at solving problems, do not give yourself an option to lose.

“我能做什么？这是不可能解决的。”
多年前，我在波士顿咨询公司实习时，曾遇到一个我觉得无法解决的问题。在这个问题上花了几天后，我放弃了。
“我认为这个问题无法解决，”我告诉我的直属上司。你猜怎么着？我被全方位抨击了。
“如果问题很简单，客户不就自己解决了吗？你认为客户雇佣我们是让我们告诉他们我们无法解决问题吗？”
我合上笔记本电脑，拿出一支笔和笔记本，开始再次尝试解决问题，但这次是用一种全新的方法。它并没有完全起作用，但我觉得我快解决问题了。我一直在努力，终于找到了答案。
我吸取了教训：没有解决不了的问题。它可能需要资源，可能需要专业知识，可能需要抓紧时间。
但你知道吗？不将“不能解决一个问题”作为一个选项时，每个问题都可以解决。
如果你想更好地解决问题，不要让自己失去选择。

Loy Machedo
There is only ONE way to improve any skill - and that is by actually doing the same task again and again and again until you become the best at it. That is the ONE way and the ONLY way to become good at anything.
When I started blogging 11 years ago - I could hardly type out 100 words if my life depended on it. It would take me 3 days to literally type out 100 words. And after the 3 days were up, I would look at the garbage I put out and I realized - this couldn’t be published. Just couldn’t.
Today I am able to come out with 2,000 words in an hour to nearly 10,000 words per day. How is this possible? Because of non-stop practice. I never stopped, I never gave up, I never ever slowed down. And when you choose to be so persistent, so obsessed and so unstoppable - you will eventually become the world’s best.

只有一种方法可以提高任何技能，那就是一次又一次地做同样的任务，直到你成为最好的。这是成为解决问题能手的唯一途径。
当我11年前开始写博客时：即使我的生活依赖于它，我几乎打不出100个字。我花了3天时间才打出100个字。3天结束后，我看着我扔出去的垃圾，我意识到，这篇文章无法发表，真的不能。
今天的我能在一小时内写出2000个字，每天能写出近10000个字。这怎么可能呢？因为不停的练习。我从不停止，从不放弃，从不放慢脚步。当你选择如此坚持，如此痴迷，如此势不可挡，你最终会成为世界上最好的。

Nela Canovic
Don’t rush to get to the end of the story. Instead, write down every chapter of the story to remember it better.
Because your problem-solving journey is exactly that — a story. And like every story, it has a certain structure, also known as an arc:
an introduction (who’s involved, where and when it’s taking place)
a triggering event (the moment when the problem shows up)
the climax (the part where the problem needs to be addressed and a decision has to be made)
after affects (when the tension from the problem starts to dissipate)
resolution (the problem is solved and lessons are learned)
How do you write your story?
Start with a notebook. It can be a journal that you’ll dedicate to only this topic. You can call it anything you wish — I like the title Obstacle Journal.

不要急于把故事写完，相反，把故事的每一章（名字）都写下来，以便更好地记住。
因为你解决问题的旅程就是这样-一个故事。就像每个故事一样，它有一个特定的结构，也被称为弧：
介绍（参与人员、地点和时间）
触发事件（问题出现的时刻）
高潮（需要解决问题并作出决定的部分）
前因后果（当问题带来的紧张开始消散）
解决方案（解决问题并吸取教训）
你是怎么写你的故事的？
从笔记本开始。它可以是一本你只专注于这个主题的日记。你可以叫它任何你想叫的名字——我喜欢叫它障碍日志。

The key to keeping this journal is to write in it every single day. It doesn’t have to take long to write, maybe 10–15 minutes at most. The daily entries don’t have to be long, either. You can organize each page into the following sections:
Top of the page — the DATE. Add the day and month here for easier tracking of entries, which will be especially useful to you later.
Section 1 — the WHAT. Write down the problem, obstacle, or mistake you made. It can be something that already happened that day, or is still going on and needs to be solved. In a few sentences, describe the situation — what happened?
Section 2 — the WHY. Write down what could have caused the problem to occur. It can be an internal factor: your behavior, a decision you made, or an interaction you had with someone. It can also be external factors that are beyond your control: someone else’s behavior, a problem caused by a larger team at work, a schedule change that affected your school curriculum, etc.
Section 3 — the LESSON. If the mistake was already made or the failure already happened, write down how you feel about it. Then think about the experience and answer these questions: What can I learn from this? How could the mistake have been avoided? What is something I didn’t consider doing that would have helped? How can I prepare for similar situations in the future so I know what to do?

写日记的关键是每天都写：不需要花很长时间来写，最多可能是10-15分钟。每天的条目也不需要太长，你可以将每个页面组织为以下部分：
页面顶部-日期。在此处添加日期和月份，以便更轻松地跟踪条目，这对您以后尤其有用。
第1节-发生什么事。写下你所犯的问题、障碍或错误。这可能是当天已经发生的事情，或者仍在发酵，需要解决。用几句话描述情况-发生了什么？
第2节-原因。写下可能导致问题发生的原因。它可能是一个内部因素：你的行为、你做出的决定或你与某人的互动。它也可能是你无法控制的外部因素：其他人的行为、工作中一个更大的团队引起的问题，时间表的改变影响了你的学校课程，等等。
第3节-教训。如果错误或失败已经发生，写下你对此的感受。然后思考经验并回答以下问题：我能从中学到什么？怎么能避免这个错误呢？有什么是我没有考虑过担会有帮助的？我如何为未来类似的情况做准备，这样我就知道该怎么做了?

Section 4 — the OPTIONS. If the problem or obstacle still exists and you need to solve it, write down three possible courses of action to choose from. Next to each one, write down what you could gain from it (the benefit) and what you may risk if you do it (the cost). Give yourself a few minutes to think through each course of action and where you anticipate the benefit to be greater than the cost.
Section 5 — the DECISION. In this section you’ll write your decision about what you’ll do next — and why. Give yourself the space to think it through. It’s important to write down your thought process so you can refer to it later. This will provide you with valuable insights into the way you solve problems so that you can make adjustments as needed.
Finally, at the end of each week, read through what you’ve written in the daily entries. You can write a short weekly summary in 3–5 sentences to note down what you’ve learned that week. You will notice certain patterns of behavior (or avoidance of things that need to be done) in the way you deal with problems. The important part is to observe what you do, identify what you can improve, and keep practicing until you get better and better at problem-solving.
That’s how you write your story.

第4节-选项。如果问题或障碍仍然存在，你需要解决它，请写下三种可能的行动方案供你选择。在每一项下，写下你可以从中获得什么（收益）以及如果你这样做可能会冒什么风险（成本）。给自己几分钟时间来思考每一个行动方案，以及你预期收益大于成本的地方。
第5节-决定。在这一节中，你将写下你下一步要做什么决定，以及为什么。给自己足够的空间去思考。写下你的思维过程很重要，这样以后就可以参考它。这将为你解决问题的方式提供有价值的见解，以便可以根据需要进行调整。
最后，在每周结束时，通读你在每日条目中写的内容。你可以用3-5句话写一个简短的每周总结，记下你那周学到的东西。在处理问题的过程中，你会注意到某些行为模式（或避免需要做的事情）。重要的部分是观察你在做什么，确定你可以改进什么，并不断练习，直到你越来越擅长解决问题。
这就是你写故事的方式。

Jamil Yousafzai
For most of the times, we jump directly to the conclusion without understanding the problems.
The best way to solve a problem is to understand the problem's statement in first. You should pay your concentration to the statement until you come to know that what is actually asked in the problem.
In university one of our professors, Dr. Professor Rahim Zada, always used to say that a problem has 50% of its solution in the statement itself. If you understand of what is being asked in the problem, 50% of the problem's solution is at your fingertip.
I don't start solution to a problem, unless I fully unnderstand it. Most of the time I spend on getting the problem, & then go towards solution.
It helps me a lot in solving any problem!

在大多数情况下，我们在不了解问题的情况下直接得出结论。
解决问题的最佳方法是首先理解问题。你应该把注意力集中在陈述上，直到你知道问题的实质是什么为止。
在大学里，我们的一位教授Rahim Zada博士经常说，一个问题有50%的解决方案在陈述中。如果你理解了题目问的问题，那么你已经解决了一半了。
除非我完全理解问题，否则我不会着手解决它，我大部分时间都花在理解问题上，然后去寻求解决方案。
这对我解决任何问题都有很大帮助！

Shawrya Mehrotra
“We cannot solve our problems with the same thinking we used when we created them.” These words by Albert Einstein accurately prove how problem-solving is integral to achieve success. Problem-solving is generally regarded as the most important analytic activity in everyday and professional contexts. Problems occur every day and cannot be escaped. Problem-solving is directly related to growth enhancement. Brushing up this skill will lead to decisiveness and empowerment, altogether. Here are some ways you can practice problem-solving skills:
KNOW YOUR PROBLEM
Before straightaway jumping on finding solutions, you should know the generic structure of your problem. What can you see that causes the problem, Where does it occur, when is it happening, why is it happening, with input from yourself and others, a series of such questions on the problem should be addressed.
BREAK DOWN THE PROBLEM
Complex problems can usually be made easier by breaking them down into smaller problems. If this process can be continued sufficiently far, you will often be left with many smaller problems which are a good deal easier to solve than the original big one.

“我们不能用创造问题时的思维来解决问题。”爱因斯坦的这句话准确地证明了解决问题是获得成功不可或缺的一部分。问题解决通常被认为是日常和专业环境中最重要的分析活动。问题每天都在发生，无法逃避。解决问题与促进增长直接相关。提高这项技能让你变得果断和有能力。以下是一些你可以练习解决问题技能的方法：
了解你的问题
在直接开始寻找解决方案之前，应该了解问题的一般结构。你能看到什么导致了问题，在哪里发生，什么时候发生，为什么发生，在你自己和他人的参与下，一系列这样的问题应该被解决。
分解问题
通过将复杂问题分解为较小的问题，通常可以使其变得更容易。如果这一过程能够持续足够长的时间，你通常会遇到许多小问题，这些问题比原来的大问题更容易解决。

ANALYZE
In this stage of problem-solving, critical input from people who have noticed the problem and who are affected by the problem should be gathered and sifted. The problem needs to viewed from a variety of viewpoints. If we don’t analyze the problem before deciding on the root cause, we could waste a lot of time, money, or other resources addressing the wrong things.
BRAINSTORM
Brainstorming helps to break out of the monotonous pattern of thinking and develop new ways to view or solve a problem. It helps you look for the practicality of all feasible solutions.
EVALUATE AND IMPLEMENT
Once you have researched well on all possible solutions, choose the best ones that according to you will cater to your problem accurately. Review various influencing factors for each possible solution and choose the solution that must be workable concerning the problem. Implement, accept and carry out the chosen course of action.
I hope my answer provided some value to the readers. Do follow me for more on education, careers, and more.

分析
在解决问题的这一阶段，应收集和筛选注意到问题和受问题影响的人的关键意见。这个问题需要从不同的角度来看待。如果我们在决定根本原因之前没有分析问题，我们可能会在错误的事情上浪费大量的时间、金钱或其他资源。
灵感
灵感有助于打破单调的思维模式，开发新的方法来看待或解决问题。它帮助你寻找所有可行解决方案的实用性。
评估和实施
一旦你充分研究了所有可能的解决方案，根据你的情况选择最适合的解决方案。审查每个可能解决方案的各种影响因素，并选择与问题相关的必须可行的解决方案。实施、接受和执行所选行动方案。
我希望我的回答能给读者提供一些价值。请关注我，了解更多关于教育、职业等方面的信息。
原创翻译：龙腾网 http://www.ltaaa.cn 转载请注明出处

Rakshit Tiwari
I am no “great” at problem solving but I can surely present a perspective to help out some people.
Its a long procedure.
In-fact, its basically nothing but a cycle which keeps on repeating and we call it life.
Goes something like this.
Analyze what you know already.
Analyze what you don’t know now.
Simple part of the equation
Start by solving problems of those type which fall in the first category.
Try to solve all of them on your own.
Share your knowledge.
Learn different methods if possible.
Make sure you remember that it was the easier part, so task is not done now.
Tougher part of the equation
Become a part of peer group which has people who know what you don’t know.

我在解决问题方面并不“优秀”，但我肯定可以提出一个观点来帮助一些人。
这是一个漫长的过程。
事实上，它基本上就是一个循环，不断重复，我们称之为生命。
大概是这样的：
分析你已经知道的；
分析你现在不知道的东西；
这只是等式的一部分；
首先解决属于第一类的问题。
试着自己解决所有问题。
分享你的知识。
如果可能，学习不同的方法。
请确保记住，这是最简单的部分，所以现在任务还没有完成。
等式中更难的部分；
成为那些知道你不知道的事情的同龄人群体的一部分。

Ask them doubts. Engage in fruitful discussions.
Learn from them.
Try solving the same problems once again.
Learn if there is still a scope.
Practice rigorously and keep on asking, learning and solving.
Fail sometimes to remember that there is still a lot to learn.
Spend more time on solving these type of problems.
Learn different methods of solving a particular problem if possible.
Become a master and share your knowledge with everybody.
Make sure you remember that it was the tougher part and you have completed the task now.
Most important aspect
You now know something more than you used to know before.
You are a better problem solver now.
Analyze once again and repeat once again. :)
Hope this helps. :)
All the best.

就疑问之处问他们意见，进行富有成效的讨论。
向他们学习。
再次尝试解决相同的问题。
看看是否还有机会；
严苛的练习，不断提问、学习和解决问题。
有时会忘记还有很多东西要学。
花更多的时间解决这类问题。
如果可能，学习解决特定问题的不同方法。
成为大师，与大家分享你的知识。
确保你记住这是最困难的部分，现在你已经完成了任务。
最重要的方面
你现在比以前知道的更多。
你现在是一个更好的问题解决者。
再次分析并再次重复。
希望这有帮助。
祝你一切顺利。

Quora Session with Academic Leaders at YUP ·
To build off Judah’s point around memorizing steps and processes, teachers should know the difference between “a process for solving this problem” and “a process for solving any problem”. The former is a procedure to apply in a specific situation, and the latter is a transferable way of thinking about math problems.
There are a number of frxworks for this, but the most effective ones develop a student’s executive function skills while doing math.
In particular, I like George Polya’s process described in his book How to Solve It (easily remembered with the acronym UPSC):
Understand: Determine what is given in a problem and what you are being asked to find. Find relevant concepts that apply and define any technical vocabulary that you’re unsure of.
Plan: Decide on a strategy in advance for solving a problem. Write it down so that you can come back to it if you get lost in the process of solving.

通过记忆步骤和过程来建立犹大的观点，教师应该知道“解决这个问题的过程”和“解决任何问题的过程”的区别。前者是适用于特定情况的程序，后者是一种可转移的思考数学问题的方式。
这方面有很多框架，但最有效的框架是在做数学时培养学生的执行能力技能。
特别是，我喜欢乔治·波利亚（George Polya）在《如何解决它》（How to Solution It）一书中描述的过程（用缩写UPSC很容易记住）：
理解：确定问题中给出的内容以及要求你查找的内容。查找适用的相关概念，定义任何不确定的技术词汇的相关概念。
计划：提前决定解决问题的策略。把它写下来，这样如果你在解决问题的过程中迷路了，你就可以再回过头来。

Solve: Execute your strategy and attend to precision. Be careful to check your work as you go along, and don’t be afraid to go back to the Plan step to find another strategy if this one doesn’t seem to be working.
Check: Is your answer reasonable in the context of the situation? Is it the only possible answer? How can I ensure that it’s accurate?
In my experience as a teacher, school leader, and now as Director of Academics here, students tend to neglect the U, P, and C parts of this, opting instead to glean basic information from the problem and rushing to put pencil to paper. Once they have an answer, they move on, relieved to be finished and sometimes even afraid of what it would mean to check and find out that they were wrong.
As teachers, it’s our responsibility to ensure that a process like this is made explicit for students and that they are constantly self-reflecting on which parts of it they are strong with and which parts are areas where they need to improve.

解决方案：执行你的策略并注意精确性。在进行过程中要仔细检查你的工作，如果这个策略似乎不起作用，不要害怕回到“计划”的步骤，寻找另一个策略。
检查：在这种情况下，你的回答合理吗?这是唯一可能的答案吗?我如何确保它是准确的?
以我作为老师、学校领导以及现在作为学术主管的经验来看，学生们往往忽略了U、P和C部分，而是选择从问题中收集基本信息，并匆忙将铅笔写在纸上。一旦他们有了答案，他们就会继续前进，为完成而感到欣慰，有时甚至害怕，因为这意味着要检查并（可能）发现他们做错了。
作为教师，我们有责任确保对学生来说是明确的，并且他们不断地自我反思哪些部分是他们的强项，哪些部分是他们需要改进的地方的这样一个过程。

Here are some examples of questions and feedback that will be more useful for a student and develop executive function skills:
Slow down when you read each sentence. Go back and reread if necessary.
Annotate the question with definitions of terms you’re unfamiliar with.
Compare your strategy with a classmate’s strategy - whose is better, and why?
Check back on your plan as you solve to make sure you’re on the right track.
How do you know that your answer makes sense?
What steps can you take to make sure that result is accurate?

以下是一些问题和反馈的示例，这些问题和反馈将对学生和发展执行能力技能更有用：
读每个句子时放慢速度。如有必要，请返回并重读。
用你不熟悉的术语的定义来注释问题。
将你的策略与同学的策略进行比较：谁的策略更好，为什么？
在解决问题的过程中回顾一下你的计划，确保你走上了正确的轨道。
你怎么知道你的答案是合理的?
你可以采取哪些步骤来确保结果是准确的？