A Mind For Numbers

| 分类 读书笔记  标签 心理学  如何学习  英文原版 

foreword

  • Your brain has amazing abilities, but it did not come with an instruction manual. You’ll find that manual in A Mind for Numbers
  • your brain will work just as hard at solving social problems as on math and science problems, if that is what has been on your mind recently

preface

  • We and other researchers have found that this passive and shallow strategy often produces minimal or no learning. We call this “labor in vain”—students are putting in labor but not getting anywhere

note to the readers

  • What takes years for practitioners to discover is now at your fingertips

Chapter 1 Open the door

  • 讲述个人经历，擅长语言的学习，因为环境所迫只能学习engineering，最后却取得博士学位。似乎很多女孩子都是擅长语言的学习，但是极少像作者这样

Chapter 2 Easy does it - Why Trying Too Hard Can Sometimes Be Part of the Problem

  • 开始讲述原理和方法，以及为什么难以学好的原因
    • 原因
      • Einstellung是牢笼也是经验，困住我们解决不了新的问题，唯有diffuse mode可破
      • 还有就是拖延给我们学习数学或者科学时造成困难
    • 方法
      • 因为两种模式每种用途不同，而我们通常只知道用focused所以让我们自己干到frustrated
      • focused mode 帮助解决已知规则的问题，diffuse mode帮助解决未知，帮你获得新的perspective，顿悟估计就从diffuse mode而来
      • 两种模式缺一不可，苦学死学不知道放松也是有副作用的。只所以有两种模式也是为了解决不同的问题，用一个三角形如何拼成正方形来举例

Focused versus Diffuse Thinking

  • You’ll be surprised at how spending a minute or two glancing ahead before you read in depth will help you organize your thoughts. You’re creating little neural hooks to hang your thinking on, making it easier to grasp the concepts
  • the two different types of networks that the brain switches between—highly attentive states and more relaxed resting state networks.1 We’ll call the thinking processes related to these two different types of networks the focused mode and diffuse mode
  • Focused-mode thinking is essential for studying math and science
  • Diffuse-mode thinking is also essential for learning math and science. It allows us to suddenly gain a new insight on a problem we’ve been struggling with and is associated with “big-picture” perspectives.Diffuse-mode insights often flow from preliminary thinking that’s been done in the focused mode.

The Focused Mode—A Tight Pinball Machine

  • Basically, the focused mode is used to concentrate on something that’s already tightly connected in your mind, often because you are familiar and comfortable with the underlying concepts。比如算乘法，规则已经了解

Why Math and Science Can Be More Challenging

  • Focused problem solving in math and science is often more effortful than focused-mode thinking involving language and people

The Diffuse Mode—A Spread-Out Pinball Machine

  • The diffuse mode has a mind of its own—you can’t simply command it to turn on
  • Ultimately, this means that relaxation is an important part of hard work—and good work, for that matter

Chapter 3 learning is creating

  • 为啥是creating？因为learning都需要diffuse mode来帮助获得新的insight，新的insgiht就是神经元的连接，这不就是create的过程吗？
  • 本章主要讲转换两种mode的技巧，以及继续阐明两种mode的功效，大量的metaphor
  • 睡眠的重要性
  • 拖延用番茄工作法
  • 所以碰到问题先focused 上场，then diffuse mode，注意每天都要学一点哪怕只有一点，沮丧了就放松。倾听自己身体的声音，不要太push自己

Shifting between the Focused and Diffuse Modes

  • one of the three B’s usually seems to do the trick: the bed, the bath, or the bus
  • Once you are distracted from the problem at hand, the diffuse mode has access and can begin pinging about in its big-picture way to settle on a solution
  • I have not failed. I’ve just found 10,000 ways that won’t work
  • In other words, just using your diffuse mode doesn’t mean you can lollygag around and expect to get anywhere
  • Consistency over time is key

General Diffuse-Mode Activators

  • Go to the gym
  • Play a sport like soccer or basketball
  • Jog, walk, or swim
  • Dance
  • Go for a drive (or tag along for the ride)
  • Draw or paint
  • Take a bath or shower
  • Listen to music, especially without words
  • Play songs you know well on a musical instrument
  • Meditate or pray
  • Sleep (the ultimate diffuse mode!)

Don’t Worry about Keeping Up with the Intellectual Joneses

  • learning slowly can mean you learn more deeply than your fast-thinking classmates

Avoid Einstellung (Getting Stuck)

  • a reminder for you that deep focused attention is an important resource that you don’t want to get pulled out of
  • Figuring out a difficult problem or learning a new concept almost always requires one or more periods when you aren’t consciously working on the problem
  • A good rule of thumb, when you are first learning new concepts, is not to let things go untouched for longer than a day
  • Working in the focused mode is like providing the bricks, while working in the diffuse mode is like gradually joining the bricks together with mortar

What to Do When You’re Really Stumped

  • People with strong self-control can have the most difficulty in getting themselves to turn off their focused mode so that the diffuse mode can begin its work

Introduction to Working and Long-Term Memory

Techie types sometimes equate short-term memory to random-access memory [RAM], and long-term memory to hard drive space

  • working memory
    • holds only about four chunks of information。所谓的focused mode其中是不是working memory一直满载？
    • like your own private mental blackboard
  • long-term memory
    • long-term memory might be thought of as a storage warehouse
    • Research has shown that when your brain first puts an item of information in long-term memory, you need to revisit it a few times to increase the chances you’ll later be able to find it when you need it

The Importance of Sleep in Learning

  • Dreaming about what you are studying can substantially enhance your ability to understand
  • Going without sleep the night before an examination can mean that even if you are perfectly prepared, your mind is simply unable to function properly

SUMMING IT UP

  • Use the focused mode to first start grappling with concepts and problems in math and science.
  • After you’ve done your first hard focused work, allow the diffuse mode to take over. Relax and do something different!
  • When frustration arises, it’s time to switch your attention to allow the diffuse mode to begin working in the background.
  • It’s best to work at math and science in small doses—a little every day. This gives both the focused and diffuse modes the time they need to do their thing so you can understand what you are learning. That’s how solid neural structures are built
  • Spaced repetition helps move items from working memory to long-term memory.
  • Sleep is a critical part of the learning process. It helps you: Make the neural connections needed for normal thinking processes—which is why - sleep the night before a test is so important.
    • Figure out tough problems and find meaning in what you are learning.
    • Strengthen and rehearse the important parts of what you are learning and prune away trivialities

Chapter 4 chunking and avoiding illusions of competence

  • 继续深入讲基础概念，以及学习方法
    • chunking其实就是为啥要先focused mode的原因
    • 形成了chunk才能占用更少的working memory
    • 以后更容易被回忆起
    • 生活中很多比如系鞋带，开车都是形成了chunk，否则遇到紧急情况的时候还要想怎么换挡就不行了
    • Solomon虽然可以一字不漏的记住所有细节但是不能形成chunk，只见树木不见森林，是不是说凡事都有利弊了？
  • Illusions of Competence，学习的误区
    • 直接看答案的话
    • 重读也会造成自己已经掌握的假象
  • Recall 和 Practice
    • 学完新东西立马recall我觉得就是练习和复习的一种，以后看文章要recall，睡前要recall
    • 练习帮助把working memory变成long term memory
    • chunk变的更加牢固
  • 之前做的不好的地方
    • 学完之后没有recall和review，印象笔记帮助我recall
    • 想省时间只看solution造成了illusions of competence

What Happens When You Focus Your Attention

  • Focused attention, in other words, can often help solve problems, but it can also create problems by blocking our ability to see new solutions(充满哲学意义)

What Is a Chunk? Solomon’s Chunking Problem

  • one of the first steps toward gaining expertise in math and science is to create conceptual chunks—mental leaps that unite separate bits of information through meaning

Basic Steps to Forming a Chunk

  • The first step in chunking, then, is to simply focus your attention on the information you want to chunk
  • The second step in chunking is to understand the basic idea you are trying to chunk
  • The third step to chunking is gaining context so you see not just how, but also when to use this chunk
    • Practice helps you broaden the networks of neurons connected to your chunk, ensuring that it is not only firm, but also accessible from many different paths
  • 形成chunk还有一个好处就是working memory可以装的更多，同时想更多的事情

Illusions of Competence and the Importance of Recall

  • Attempting to recall the material you are trying to learn—retrieval practice—is far more effective than simply rereading the material(reread造成已经掌握的假象)
  • Using recall—mental retrieval of the key ideas—rather than passive rereading will make your study time more focused and effective
  • 特别是只看答案自己没有想出来，自己之前学数学就是如此。那个时候学的好估计是因为每周recall学了什么
  • The bigger your chunked mental library, the more easily you will be able to solve problems

Practice Makes Permanent

  • The more you practice, the firmer, darker, and stronger your mental patterns become
  • In the same amount of time, by simply practicing and recalling the material, students learned far more and at a much deeper level than they did using any other approach
  • the retrieval process itself enhances deep learning and helps us begin forming chunks
  • 思维导图一开始就用并不好。It’s like trying to learn advanced strategy in chess before you even understand the basic concepts of how the pieces move
  • 终身努力便成天才

Interleaving—Doing a Mixture of Different Kinds of Problems—versus Overlearning

  • Interleaving means practice by doing a mixture of different kinds of problems requiring different strategies
  • Continuing the study or practice after it is well understood is called overlearning，it can be a waste of valuable learning time
  • You want your brain to become used to the idea that just knowing how to use a particular problem-solving technique isn’t enough—you also need to know when to use it.
  • Once they understand ‘X,’ they should move on to something else and return to ‘X’ on another day
  • There’s evidence that writing by hand helps get the ideas into mind more easily than if you type the answer
  • 做这章练习的时候都是同一类型，那么可以回到上一章做做前面的练习

SUMMING IT UP

  • Practice helps build strong neural patterns—that is, conceptual chunks of understanding
  • Practice gives you the mental fluidity and agility you need for tests.
  • Chunks are best built with
    • Focused attention
    • Understanding of the basic idea
    • Practice to help you gain big-picture context
  • Simple recall—trying to remember the key points without looking at the page is one of the best ways to help the chunking process along

Chatper 5 preventing procrastination

  • 为啥有procrastination
    • things that make us feel uncomfortable
    • Procrastination is like addiction. It offers temporary excitement and relief from boring reality
  • 影响
    • 影响心理和生理健康
    • The dread of doing a task uses up more time and energy than doing the task itself
  • 如何克服
    • You should have been studying a little bit all along
    • 专注过程而不是结果
  • For most people, learning math and science depends on two things: brief study sessions where the neural “bricks” are laid, and time in between for the mental mortar to dry
  • SUMMING IT UP
    • We procrastinate about things that make us feel uncomfortable. But what makes us feel good temporarily isn’t necessarily good for us in the long run
    • Procrastination can be like taking tiny amounts of poison. It may not seem harmful at the time. But the long-term effects can be very damaging

Chapter 6 zombies everywhere

  • 如何克服拖延
    • 本质上是改变习惯
    • 关注process不是product
    • 改变信念
    • 利用想象力，想象成功的模样
  • Habits can be good and bad. Habit, after all, is simply when our brain launches into a preprogrammed “zombie” mode
  • Habit is an energy saver for us. It allows us to free our mind for other types of activities
  • habits 4 parts
    • the cue
    • rountine
    • reward
    • belief

      Harnessing Your Habits (Your “Zombies”) to Help You

  • The only place you need to apply willpower is to change your reaction to the cue ，之后的事情便水到渠成
  • Belief that your new system works is what can get you through
  • A powerful approach is mental contrasting. In this technique, you think about where you are now and contrast it with what you want to achieve。利用想象力和希望

Get into the Flow by Focusing on Process, Not Product

  • If you find yourself avoiding certain tasks because they make you uncomfortable, there is a great way to reframe things: Learn to focus on process, not product
  • By focusing on process rather than product, you allow yourself to back away from judging yourself (Am I getting closer to finishing?) and allow yourself to relax into the flow of the work
  • Multitasking is like constantly pulling up a plant. This kind of constant shifting of your attention means that new ideas and concepts have no chance to take root and flourish
  • Use the twenty-five-minute Pomodoro to stay productive for brief periods. Then reward yourself after each successful period of focused attention
  • Be sure to schedule free time to nurture your diffuse mode

Chapter 7 chunking versus choking

  • powerful chunk的优点
    • Increase Your Expertise and Reduce Anxiety
  • 如何形成powerful chunk
  • 见下方how to build,概括为recall, test, repetition, rest. 2r2t 学习中碰到的其他困难
  • choking
    • working memory不够用
  • knowledge collapse
    • 之前的理解可能有问题，知识重构ing
  • 让人想到读书，如果读书不复习的确就忘记了。但是如果每本书都反复读时间不够。只读经典，泛读案例
  • Enhancements come only after an invention has been out for a while and people have had a chance to mess with it.所以很多事情都要先做，再优化

How to Build a Powerful Chunk

  • Learning fundamental concepts of math and science can be a lot easier than learning subjects that require a lot of rote memorization
  • STEPS TO BUILDING A POWERFUL CHUNK
    • Work a key problem all the way through on paper
    • Do another repetition of the problem, paying attention to the key processes
    • Take a break(You need to give your diffuse mode time to internalize the problem)
    • Sleep. Before you go to sleep, work the problem again
    • Do another repetition
    • Add a new problem
    • Do “active” repetitions
  • Generating (that is, recalling) the material helps you learn it much more effectively than simply rereading it(之前R programming的练习如果没有重做估计也都忘记了，必须重做两次)
  • A master violinist, for example, doesn’t just play a musical piece from beginning to end, over and over again. Instead, she focuses on the hardest parts of the piece
  • The difference between lesser-ranked players and grand masters is that grand masters devote far more time to figuring out what their weaknesses are and working to strengthen those areas（刻意的练习）

Hitting the Wall—When Your Knowledge Suddenly Seems to Collapse

  • This type of “knowledge collapse” seems to occur when your mind is restructuring its understanding—building a more solid foundation（马德俊曾经说过，当时不理解）
  • Choking—panicking to the point where you freeze—can happen when your working memory is filled to capacity, yet you still don’t have enough room for the additional critical pieces you need to solve a problem
  • Testing in itself is a powerful learning experience. It changes and adds to what you know, also making dramatic improvements in your ability to retain the material（读书要身临其境就是test）
  • interaction with peers as well as instructors helps with the learning process

summing it up

  • Chunking means integrating a concept into one smoothly connected neural thought pattern
  • Chunking helps increase the amount of working memory you have available
  • Building a chunked library of concepts and solutions helps build intuition in problem solving
  • When you are building a chunked library, it’s important to keep deliberate focus on some of the toughest concepts and aspects of problem solving
  • Occasionally you can study hard and fate deals a bad hand. But remember the Law of Serendipity: If you prepare well by practicing and building a good mental library, you will find that luck will be increasingly on your side. In other words, you guarantee failure if you don’t try, but those who consistently give it a good effort will experience many more successes

Chapter 8 tools, tips, and tricks

  • 让自己更加专注可以通过营造环境，去图书馆或者和别人一起学习，也可以通过让电脑、手机免打扰模式
  • 通过GTD安排周计划，日计划减少workimg memory的压力，更加高效
  • 以上两种都是让自己的zombie帮助自己
  • a special place devoted just to working is particularly helpful
  • Another trick involves using meditation to help you learn to ignore distracting thoughts.3 (Meditation is not just for New Age types—a lot of science has revealed its value
  • A last important trick is to reframe your focus
  • “It’s normal to sit down with a few negative feelings about beginning your work. It’s how you handle those feelings that matters

Ultimate Zombie Alliance: The Planner-Journal as Your Personal Lab Notebook

  • Once a week, write a brief weekly list of key tasks. Then, each day, write a list of the tasks that you can reasonably work on or accomplish. Try to write this daily task list the evening before
  • Planning your quitting time is as important as planning your working time
  • It’s important to transform distant deadlines into daily ones

SUMMING IT UP

  • Mental tricks can be powerful tools. The following are some of the most effectiv
    • Put yourself in a place with few interruptions, such as a library, to help with procrastination.
    • Practice ignoring distracting thoughts by simply letting them drift past
    • If your attitude is troubled, reframe your focus to shift attention from the negative to the positive
    • Realize it’s perfectly normal to sit down with a few negative feelings about beginning your work
  • Planning your life for “playtime” is one of the most important things you can do to prevent procrastination, and one of the most important reasons to avoid procrastination
  • At the heart of procrastination prevention is a reasonable daily to-do list, with a weekly once-over to ensure you’re on track from a big-picture perspective
  • Write your daily task list the evening before

Chapter 9 procrastination zombie wrap-up

  • 本章依然讨论拖延
  • 很多人兴起就工作很久，但是不想干就不干，这样从总体上看可能并没有按照计划每天走的人效率高
  • 关于willpower的观点，和我之前想的一样。和肌肉一样越练越强，现在的我比上高中、大学好了很多，也了解了更多技巧和方法。总体上而言一句话：凡事预则立
  • passion这个词被很多人用烂了，如果我们做的好有回报自然有passion，passion和兴趣一样可以培养

The Pluses and Minuses of Working Unrelentingly in “The Zone

  • People who make a habit of getting their work done in binges are much less productive overall than those who generally do their work in reasonable, limited stints. Staying in the zone too long will send you toward burnout

wise waiting

  • Pausing and reflecting are key
  • Staving off natural desires to react aggressively to emotional provocations allows time for the molecules of emotion to gradually dissipate. The resulting cooler heads save lives
  • In choosing your career, for example, “Follow your passion” may be like deciding to marry your favorite movie star
  • Over the past decades, students who have blindly followed their passion, without rational analysis of whether their choice of career truly was wise, have been more unhappy with their job choices than those who coupled passion with rationality
  • We develop a passion for what we are good at

SUMMING IT UP

  • Keep a planner-journal so you can easily track when you reach your goals and observe what does and doesn’t work.
  • Commit yourself to certain routines and tasks each day
  • Write your planned tasks out the night before, so your brain has time to dwell on your goals to help ensure success.
  • Arrange your work into a series of small challenges. Always make sure you (and your zombies!) get lots of rewards. Take a few minutes to savor the feelings of happiness and triumph
  • Deliberately delay rewards until you have finished a task.
  • Watch for procrastination cues
  • Put yourself in new surroundings with few procrastination cues, such as the quiet section of a library
  • Obstacles arise, but don’t make a practice of blaming all your problems on external factors. If everything is always somebody else’s fault, it’s time to start looking in the mirror.
  • Gain trust in your new system. You want to work hard during times of focused concentration—and also trust your system enough that when it comes time to relax, you actually relax without feelings of guilt.
  • Have backup plans for when you still procrastinate. No one is perfect, after all
  • Eat your frogs first

Chapter 10 enhancing your memory

  • 讲的都是memory的技巧，之前的我只是将理解的公式记住。但是通过图片或者将不熟悉的东西和熟悉的东西联系起来会更加容易记住比如公式，周期表等难记的东西。当然这之间的联系需要自己想象

Can You Remember Where Your Kitchen Table Is? Your Supersized Visuospatial Memory

  • The image helps you encapsulate a seemingly humdrum and hard-to-remember concept by tapping into visual areas with enhanced memory abilities(ppt要用图的原因？)
  • The more neural hooks you can build by evoking the senses, the easier it will be for you to recall the concept and what it means

The Memory Palace Technique

  • 先把数字和实物建立联系，再和位置建立联系。总体上来说就是尽量多的建立联系，以便日后记起来

summing it up

  • The memory palace technique—placing memorable nudges in a scene that is familiar to you—allows you to dip into the strength of your visual memory system
  • Learning to use your memory in a more disciplined, yet creative manner helps you learn to focus your attention, even as you create wild, diffuse connections that build stronger memories
  • By memorizing material you understand, you can internalize the material in a profound way. And you are reinforcing the mental library you need to become a genuine master of the material

Chapter 11 More Memory tips

  • 听说读写练
  • 听：用歌曲
  • 说：talk to yourself
  • 读：用脑子读，用metphor
  • 写：用手写
  • 练：锻炼身体，记得重复练习

Spaced Repetition to Help Lodge Ideas in Memory

  • Much of what goes on around you is basically trivial—if you remembered it all, you’d end up like a hoarder, trapped in an immense collection of useless memories
  • Repetition is important; even when you make something memorable, repetition helps get that memorable item firmly lodged in long-term memory

Create Stories

  • The number one thing I stress when students come to see me is that there is a direct connection between your hand and your brain, and the act of rewriting and organizing your notes is essential to breaking large amounts of information down into smaller digestible chunks
  • Talk to yourslef
  • regular exercise can make a substantive improvement in your memory and learning abilities

SUMMING IT UP

  • Metaphors can help you learn difficult ideas more quickly.
  • Repetition is critical in allowing you to firm up what you want to remember before the ideas fade away.
  • Meaningful groups and abbreviations can allow you to simplify and chunk what you are trying to learn so you can store it more easily in memory.
  • Stories—even if they are just used as silly memory tricks—can allow you to more easily retain what you are trying to learn.
  • Writing and saying what you are trying to learn seems to enhance retention.
  • Exercise is powerfully important in helping your neurons to grow and make new connections

Chapter 12 learning to appreciate your talent

  • 每个人都有自己的长处
  • 聪明的人固然working memory更大，但是也有自己的问题，心智可能成熟的晚，碰到没遇到的问题容易恐慌，创造力可能一般
  • 而且working memory可以通过练习得到提高，只要肯付出，可以练习，一切都可以克服
  • 我自己我感觉并不是特别聪明的人，但是很会融会贯通，学某样新的东西我接受的不是特别快，但是过段时间我的chunk一直在，而且和别的chunk都有联系

Work toward an Intuitive Understanding

  • Chess masters, emergency room physicians, fighter pilots, and many other experts often have to make complex decisions rapidly. They shut down their conscious system and instead rely on their well-trained intuition

No Need for Genius Envy

  • Being smarter often equates to having a larger working memory
  • People with less apparent intellectual horsepower, on the other hand, can cut more easily to simpler solutions
  • Being smart makes it more difficult for you to be creative
  • You may have to work harder sometimes (or even much of the time) to understand what’s going on, but once you’ve got something chunked, you can take that chunk and turn it outside in and inside round—putting it through creative paces even you didn’t think you were capable of!
  • It is the practice—particularly deliberate practice on the toughest aspects of the material—that can help lift average brains into the realm of those with more “natural” gifts
  • Extremely smart people are more likely than people of normal intelligence to procrastinate because it always worked when they were growing up, which means they are less likely to learn certain critical life skills early on

SUMMING IT UP

  • At some point, after you’ve got chunked material well in hand (and in brain), you start to let go of conscious awareness of every little detail and do things automatically.
  • It may seem intimidating to work alongside other students who grasp material more quickly than you do. But “average” students can sometimes have advantages when it comes to initiative, ability to get things done, and creativity
  • Part of the key to creativity is to be able to switch from full focused concentration to the relaxed, daydreamy diffuse mode
  • Focusing too intently can inhibit the solution you are seeking—like trying to hammer a screw because you think it’s a nail. When you are stuck, sometimes it’s best to get away from a problem for a while and move on to something else, or to simply sleep on it

Chapter 13 sculpting your brain

  • 以卡扎尔为例说明了人脑是可以发生巨变的
  • 脑子里的神经连更多，chunk更多
  • 这样学习别的事物时更加方便。融会贯通之后就像打通任督二脉，学习会越来越顺利
  • 人的脑子可能在20多岁才会发育成熟，之前可能就是学渣，后来变学霸

Change Your Thoughts, Change Your Life

  • This may explain why teenagers often have trouble controlling their impulsive behavior—the wiring between intention and control areas imppulsive behavior—the wiring between intention and control areas isn’t completely formed
  • One might say that work substitutes for talent, or better yet that it creates talent
  • we can make significant changes in our brain by changing how we think
  • Good chunks form neural patterns that resonate, not only within the subject we’re working in, but with other subjects and areas of our lives. The abstraction helps you transfer ideas from one area to another
  • One important key to learning swiftly in math and science is to realize that virtually every concept you learn has an analogy—a comparison—with something you already know

Summing it up

  • Brains mature at different speeds. Many people do not develop maturity until their midtwenties
  • Some of the most formidable heavyweights in science started out as apparently hopeless juvenile delinquents
  • One trait that successful professionals in science, math, and technology gradually learn is how to chunk—to abstract key ideas.
  • Metaphors and physical analogies form chunks that can allow ideas from very different areas to influence one another.
  • Regardless of your current or intended career path, keep your mind open and ensure that math and science are in your learning repertoire. This gives you a rich reserve of chunks to help you be smarter about your approach to all sorts of life and career challenges

Chapter 14 developing the mind’s eye through equation poems

  • 知识内化的过程，如何向别人解释，向自己解释？如果没有做到这一步，那些知识很快就会遗忘
  • 学习完了写总结和ppt讲给别人听是很好的方式
  • 周末复习的时候用用，把复杂的公式用自己的方式理解，看reddit和explain等网站看看别人如何内化知识的
  • 这其实也是我一直使用的方式，用更加直观的方式理解复杂的东西，不过有些东西很难。比如4维图形

art and science

  • There are hidden meanings in equations, just as there are in poetry
  • A mathematician who is not at the same time something of a poet will never be a full mathematician
  • scientists often see equations as a form of poetry, a shorthand way to symbolize what they are trying to see and understand

Simplify and Personalize Whatever You Are Studying

  • One of the most important things we can do when we are trying to learn math and science is to bring the abstract ideas to life in our minds
  • This is why teachers often say that the first time they ever really understood the material was when they had to teach it

Transfer—Applying What You’ve Learned in New Contexts

  • Students who interrupt their work constantly not only don’t learn as deeply, but also aren’t able to transfer what little they do learn as easily to other topics

SUMMING IT UP

  • Equations are just ways of abstracting and simplifying concepts. This means that equations contain deeper meaning, similar to the depth of meaning found in poetry
  • Your “mind’s eye” is important because it can help you stage plays and personalize what you are learning about
  • Transfer is the ability to take what you learn in one context and apply it to something else
    • It’s important to grasp the chunked essence of a mathematical concept, because then it’s easier to transfer and apply that idea in new and different ways
    • Multitasking during the learning process means you don’t learn as deeply—this can inhibit your ability to transfer what you are learning

Chapter 15 renaissance learning

  • 颠覆关于学习的许多偏见，也让也多人更加有信心
  • 有些人反应很快，但是慢并不见得不好，因为可能考虑的更加细微，到时可能印象也更深刻
  • 接触些比你牛的人，也许一句话就能改变你的看法，提升你的境界
  • 自学并不一定比在学校学习效果差，Persistence is often more important than intelligence
  • Persistence is often more important than intelligence
  • Research has shown that students learn best when they themselves are actively engaged in the subject instead of simply listening to someone else speak
  • College isn’t the only way to learn. Some of the most powerful and renowned people of our time, including powerhouses Bill Gates, Larry Ellison, Michael Dell, Mark Zuckerberg, James Cameron, Steve Jobs, and Steve Wozniak, dropped out of college
  • Taking responsibility for your own learning is one of the most important things you can do

The Value of Great Teachers

  • a simple sentence growing from their vast experience can change the course of your future. And also be sure to show appreciation for the people guiding you—it is essential to let them know that the help is meaningful
  • Truly great teachers make the material seem both simple and profound, set up mechanisms for students to learn from each other, and inspire students to learn on their own
  • It seemed their introversion made them more thoughtful and sensitive to others, and their humble awareness of their past failings gave them patience and kept them from becoming aloof know-it-alls

The Other Reason for Learning on Your Own—Quirky Test Questions

  • These students unfortunately sometimes think of themselves as not very bright, but the reality is that their slower way of thinking can allow them to see confusing subtleties that others aren’t aware of

SUMMING IT UP

  • Learning on your own is one of the deepest, most effective ways to approach learning:
    • It improves your ability to think independently.
    • It can help you answer the strange questions that teachers sometimes throw at you on tests
  • In learning, persistence is often far more important than intelligence
  • Train yourself to occasionally reach out to people you admire. You can gain wise new mentors who, with a simple sentence, can change the course of your future. But use your teachers’ and mentors’ time sparingly
  • If you aren’t very fast at grasping the essentials of whatever you are studying, don’t despair. Surprisingly often, “slower” students are grappling with fundamentally important issues that quicker students miss. When you finally get what’s going on, you can get it at a deeper level
  • People are competitive as well as cooperative. There will always be those who criticize or attempt to undermine any effort or achievement you make. Learn to deal dispassionately with these issues

Chapter 16 avoiding overconfidence

  • 通过一个右脑出现功能障碍的例子来说明foucsed mode带来的问题，以及正常人如何避免
  • focused mode会让人overconfidence，坚信自己是正确的。这个时候需要用左脑来帮助自己检查，用bigger picture。这也是为什么做任何事情要反复检查的原因，要brain storm的原因，多个大脑来帮助你
  • 以后做任何事情，做完回想思考改进,同时保持谦虚，不要事事认为自己都对的

The Power of Teamwork

  • There’s a great deal of evidence from research that the right hemisphere helps us step back and put our work into big-picture perspective
  • when you whiz through a homework or test problem and don’t go back to check your work, you are acting a little like a person who is refusing to use parts of your brain
  • When you step back and recheck, you are allowing for more interaction between hemispheres—taking advantage of the special perspectives and abilities of each
  • The first principle is that you must not fool yourself—and you are the easiest person to fool

The Value of Brainstorming with Others

  • But acquaintances such as class teammates tend to run in different circles—meaning that your access to the “outside your brain” interpersonalsonal diffuse mode is exponentially larger
  • In a related vein, people often don’t realize that competition can be a good thing—competition is an intense form of collaboration that can help bring out people’s best

summing it up

  • The focused mode can allow you to make critical errors even though you feel confident you’ve done everything correctly. Rechecking your work can allow you to get a broader perspective on it, using slightly different neural processes that can allow you to catch blunders
  • Working with others who aren’t afraid to disagree can:
    • Help you catch errors in your thinking.
    • Make it easier for you to think on your feet and react well in stressful situations
    • Improve your learning by ensuring that you really understand what you are explaining to others and reinforcing what you know
    • Build important career connections and help steer you toward better choices
  • Criticism in your studies, whether you are giving or receiving it, shouldn’t be taken as being about you. It’s about what you are trying to understand
  • It is easiest of all to fool yourself

Chapter 17 test taking

  • test的好处以及如何面对test
  • 帮助自己更快的学习东西，比看资料好很多
  • 但是要面对考试带来的压力，可以通过writing或者其他自己的方式释放
  • Testing is itself an extraordinarily powerful learning experience

The Hard-Start–Jump-to-Easy Technique

  • The answer is to start with the hard problems—but quickly jump to the easy ones

Why Anxiety Can Arise on Tests and How to Deal with It

  • We think that writing helps to release negative thoughts from mind, making them less likely to pop up and distract you in the heat of the moment

Chapter 18 unlock your potential

如何灵活应用以及本书总结

  • your desire to figure things out right now is what prevents you from being able to figure things out
  • Reshaping your brain is under your control. The key is patient persistence—working knowledgeably with your brain’s strengths and weaknesses
  • The relaxation periods provide time to gain perspective—to synthesize both the context and the big picture of what we are doing
  • Indeed, our ability to fool ourselves is part of why we check back—Does this really make sense
  • students in math and science can’t develop solid neural chunks if they procrastinate in their studies

TEN RULES OF GOOD STUDYING

  • Recall
  • Test yourself
  • Chunk your problems
  • Space your repetition
  • Alternate different problem-solving techniques during your practice
  • Take breaks
  • Use explanatory questioning and simple analogies
  • Focus
  • Eat your frogs first. Do the hardest thing earliest in the day, when you are fresh
  • Make a mental contrast

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