Use the right brain, no longer afraid of numbers | Book Review

Learn how to learn, and how to think creatively and solve (almost) any problem

"With the right brain, no longer afraid of numbers: learn how to learn, and how to think creatively, to solve (almost) all problems" (hereinafter referred to as " use the right brain, no longer afraid of numbers ") The original book titled " A Mind for Numbers " by Barbara Oakley, Ph. D, translated by Huang Jiayu. Published by Trojan Culture Co., Ltd. in October 2015. It is worth noting that the second edition of this book changed the title and changed it to "The Brain Likes to Learn: Know Your Brain First, Find the Right Thinking Path, You Can Focus, Don't Procrastinate, Improve Your Memory, and Learn How to Learn" (hereinafter referred to as "The brain likes to learn this way "), the original title and Chinese translation remain unchanged; the second edition was also published by Trojan Culture Co., Ltd. on September 27, 2017.

This is a book about how Mathematical Diaosi or Lu She successfully counterattacked (and greatly). On the first 21 pages, the author vividly and meticulously described how she hated and hated mathematics and science subjects since she was a professional soldier before she returned to school after being discharged from the military in the United States (of course, the teachers who taught these subjects naturally treated him badly) ; Because of her refusal to study mathematics and physics, she failed to pass mathematics until she was twenty-six years old, and she also began to learn trigonometry at the age of twenty-six.

Since then, the author, on the one hand, for the needs of career development after being discharged from the army, on the other hand, also saw the benefits of his military colleagues who are good at mathematics and physics, so he decided to launch a challenge: retrain his brain, so that It can thoroughly understand and know how to learn mathematics. It had been seven years since her first year of high school. It is not easy to return to school to study again, not to mention that I have chosen electrical engineering related to mathematics, which I have never understood and failed to pass in the past 26 years. However, we can also say that without such a great turning point, it would not have been possible for the author to create this book after successfully changing his cognitive mode of learning, and then to create this book for many students who have been tormented by mathematics or science (I am a very obvious and Painful witnesses) kindle a light of hope and light.

This book is not only for "people who are afraid of mathematics" (the author's original words), but also for mathematics experts. Regardless of the degree or reason, we want to continue to be more sophisticated in our functional specialties and preferences. This book focuses on the causal relationship between learning methods (especially the discoveries of brain science) and achievement, plus the author's personal experience of introspection and research for 40 years, the sharing of these first-hand successful experiences plus The content and methods are highly operable, which makes this book worth reading.

The first 20 or so pages begin with Babara Oakley's journey from childhood, high school and elementary school, when mathematics was rotten to nothing, and then through her specializing in Russian, she served in the US military until she was discharged from the army and entered university, and started a solid review of the whole book. , discussion, and teaching. I have divided the main points of this book into the following three parts:

1. What happens to your brain (mainly) when you study

(1) Understand “focused mode” and “diffuse” thinking

We use mindful thinking a lot: when you're seriously writing an exam, listening to a lecture, or even reading this review of my book, you're using it. In the author's words: It's like focusing the light of a flashlight somewhere in a dark room so that you can see it carefully.

Divergent thinking usually goes unnoticed, but it is as integral to cognitive ability as it is to understanding long-term knowledge. Although often overlooked, divergent thinking, like focused thinking, fills our lives and brains almost every day. When you can't solve some problems and can't find a way to break through some relationships, you may be tired or tired of thinking about the same thing constantly and do something else; for example: take a walk, walk the dog , exercise, sleep, or play a LOL (online game) game with friends. You actually remember the original problem, but you are no longer fully focused on it. But the brain doesn't forget or put it aside, it continues to process it, but we don't notice it. In the author's words:

Meticulous and focused attention is more strongly associated with the left hemisphere, which appears to be responsible for processing organized information and logical thinking, step-by-step. The right hemisphere is more inclined to scan the environment, interact with people, manage emotions, and is in charge of taking control of the big picture and processing the multiple influx of information at the same time.

But this does not mean that some people are more developed on the left side of the brain (so they are strong in science and engineering), and some people only have more developed right brains (thus in literature and history):

...but be careful about the so-called "left-brained people" and "right-brained people" - because research shows that this is not the case at all...whether it is focused or divergent thinking, both sides of the brain must be used. .

You've probably heard many examples of great discoveries or inventions after divergent thinking. For example: German chemist August Kekulé (Chinese: August Kekulé, full name Friedrich August Kekulé von Stradonitz) pondered the carbon structure in benzene compounds for a long time, and finally, in a tired sleep after research, " I dreamed that the benzene ring structure was discovered when a snake was connected end to end. And this legendary dream stemmed from his years of research on carbon-carbon bonds. ” In addition, people from various fields such as Edison and Jane Austen, Divergent thinking (even if they don't know the term in their fashion) is also commonly used for walks, baths, rides, or playing with an iron ball in the palm of their hands for inspiration and more.

In fact, focused thinking and divergent thinking have always alternated and played a role in our lives, and both are indispensable. Based on the research results and experience obtained, the author further proposes that if you want to think divergently, you have to "relax", at least from the ongoing focused thinking. It is also possible to change to another subject or business to focus on thinking, but it is better to be as far as possible from the previous focused thinking project. But the so-called "rest" can't be too long and absurd.

…The rest periods in between periods of focused effort must be frequent enough that the mind completely forgets the problem you are dealing with. Usually a few hours are enough to make significant progress in divergence, and not so often that you forget what you've learned the next time you re-enter focused mode. As a rule of thumb, don't go more than a day without touching what you're trying to learn if you're exposed to a new concept.

(2) There must be an appropriate focused thinking process before divergent thinking.

The vast majority of human beings are naturally inclined to indulge and dislike labor. This is not the original sin, but the genetic characteristics endowed by nature. If ancient humans did not choose the "principle of least resistance" to live, they could easily exhaust their physical strength and die. But "now is not what it used to be", now we don't have to spend too much time paying attention to the beasts around or the raids of others, and more time and "brain power" can be invested in learning new things.

Since the "divergent thinking" mentioned above is so good, is it better to walk, sleep, and play electric games every day? No, not at all.

...Using divergent mode doesn't mean you can mix things up and think there's progress. Day by day, a balanced practice (switching back and forth between the mindful focus mode and the relaxed diverging mode) can achieve the learning effect.

...you have to work hard in Concentrated Mode beforehand, but the sudden and unexpected answer that emerges in Divergent Mode can be called an epiphany.

The epiphany that comes with divergent thinking often emerges from the initial insights gained from prior thinking in a focused mode.

… Business leaders like Bill Gates, for example, will deliberately set aside a week of doing nothing but reading, so that their brains are intensively exposed to all kinds of ideas during this time. They then create connections between ideas, thereby fostering innovative thinking. (By the way: the biggest difference between a creative scientist and a technically capable but imaginative one is having a broad range of interests.) The bigger the library of chunks in your head—memory ribbons will longer and longer.

In other words: if you want to think divergently, you have to "have something to think about". Even though Hui Neng, the sixth patriarch of Chinese Zen, can't read a word, and only "piles up rice and breaks firewood" every day, he can still achieve enlightenment, but he is a rare person in the ages. Readers, please don't think that you can compare. The learning and growth of ordinary people still have to start with focused learning, and then use divergent thinking for rumination and internalization.

2. The right way to learn - make good use of "recall" and "self-test"

(1) Deliberate "use of recall" and "self-testing"

The author acknowledges that extensive practice is necessary and is one of the important ways to learn new knowledge and skills.

...a lot of practice math problems can help you understand what to use such a problem-solving program and why it works. ...after understanding the basic concepts, it is easier for you to apply existing knowledge to new questions. This kind of bypass phenomenon is called transfer, ...

However, it is similar to the author of "Deliberate Practice: A Comprehensive Analysis of the Original Creator, a Learning Method More Critical Than Talent" (hereinafter referred to as " Deliberate Practice ", the original title is "Peak: Secrets from the New Science of Expertise" ): no A lot of practice in reviewing (or the more recent term "overturning") is wasted effort. If you read the same math problems over and over again, even if you have done the whole book a hundred times, you are only familiar enough with the existing problems to memorize them. This does not mean that you have "understood" the reasoning behind it at all. When the narrative or logic of the problem changes slightly, you are more likely to eat turtles. The book refers to this almost pointless repetition and the resulting "I get it" feeling of good self as "illusions of competence."

...many students experience "illusions of competence" as they learn. Jeffrey Karpicke said: "Many students will "repeatedly read their notes or textbooks (in fact, the learning effect of this is very limited), but few people test how much they have learned, and there is very little retrieval practice."

…Believing you understand just by looking at the answers is the most common illusion of competence in learning.

In the words of the Chinese world notice: "Learning without thinking is ineffective, thinking without learning is perilous" (The Analects of Confucius, Weizheng), and in "Deliberate Practice", it emphasizes "practice with a goal." So, what kind of mass practice is really beneficial? The author points out two points: First, use recall. Second, test yourself frequently. The two are actually very similar in nature: they are both asking and answering questions after closing the book and leaving the environment where the answers are available, to see how much they remember or can apply what they have learned.

A research report published in the important scientific journal "Science" provides strong evidence for the above statement. A group of students study a natural science textbook, then try to recall the content, reread it, and recall it again (that is, try to recall the main points of the book). ...by simply reviewing and recalling the main points of the text, you can learn more and understand more deeply than other methods, and the effect is far better than reading the textbook repeatedly, or drawing a concept map that logically helps to integrate the learning content. ).

In addition to the textbook, changes in the environment are also part of the self-test. Many people often say that they are easily nervous in exams, and that they fail in exams because they are abnormal in unfamiliar exam rooms; in recent years, most of the books on habit development also mention research or conclusions on "environmental cues". That is: the more often people work, read, or engage in certain life patterns in the same environment, and over time, the more likely they are to "habitually automatically" do what they would do there whenever they enter that environment. . For example, when you get up in the morning, you usually brush your teeth first when you walk into the bathroom, and I may take a shower first; some people go to the coffee shop to write a diary, and some people go to a certain seat in the study room of the library to concentrate on reading.

Therefore, if you want to confirm whether you have really internalized new knowledge or skills and are ready to use, you can change the location of learning, recall, or self-testing in a timely manner. If you can use it freely in every place, not only do you not have to worry about not learning it, but you also don’t have to worry about the so-called “on-the-spot malfunction”.

...if you train yourself to recall course content in a variety of contexts, you won't be limited to specific contextual cues, and you'll avoid the confusion caused by the difference between the exam room and the reading environment.

(2) Practical points of "recalling the memory" and "self-examination"

1. Be careful when you focus: the moment you focus is actually focused thinking, and the impression you absorb at that time will become the raw material for divergent thinking later, so you must not be careless. There is a saying in the academic world: "When you refer to everything, you actually refer to nothing." Therefore, the key points should not be long and short. The author has the following suggestions:

Train yourself to find the key points before drawing, and try to draw the line as well as possible - no more than one sentence in each paragraph. In contrast, it is a good reminder to summarize important concepts first, and then take notes in the blanks of the page.

Some students paste their written solutions to the exercises on the relevant pages of their textbooks, making the information immediately available. (If the textbook needs to be returned, use non-marking tape or post-it notes.) Writing down the answers by hand is an important act. …Alternatively, keep important questions and solutions together in the same folder for your general review before the exam. .

If you don't own the book, buy reusable post-it notes. The investment in buying 3M Post-it notes is definitely a lot better and cost-effective than buying an iPad or Macbook Pro to take notes (the author believes that writing and taking notes by hand and pen and paper is better than typing, and presents research results to support it).

2. Use recall a lot: The easiest way is to think about what you have learned in the past 20 minutes or 50 minutes (depending on whether you have used the "Pomodoro Technique"). Can you remember the big title, continue to recall, and can use your own words to show the logic and the reason and process of derivation in this or that way.

3. Try to do it on your own: What I'm talking about here is: don't memorize it, and don't read the question and read the answer and think "I can do it" before thinking that you can do it; especially mathematics and science subjects. There is an answer, of course, you can look at it when you are puzzled, but at the same time, it will also give you the opportunity to "recite the answer". In the process of learning mathematics and science, whether the deduction process is correct is the most important thing, which is why some mathematics and science teachers in school give "sympathy points": even if the answer is wrong, if the deduction process is correct or the thinking is generally fine , there will still be a few points.

4. Find a way to review the course content on the day of study: The author uses more of his own experience to discuss here. But in fact, "it is best to review within a day" is based on the results of psychological experiments. The famous "forgetting curve " is an example. The forgetting curve was first proposed by Hermann Ebbinghaus , which proves that the time when a brand-new memory is most forgotten (that is, the steepest graph) is before the first day of learning (if you don’t review it on the first day, about 74% will be forgotten). forget). So at least review it once before going to bed on the day you finish learning new knowledge .

3. The practical content of a good learning cycle

As said at the beginning of this article: "Use the right brain, no longer afraid of numbers" emphasizes "deliberate" and "planned" review. But concepts and theory alone are not enough for this book to be admired by me and many others. Another thing that makes it worth reading is that it is "extremely operational." This paragraph is to organize the essence of this part:

(1) It’s better to be tight than to learn : Many people will study the same subject or the same field for more than ten hours in a day, because the mid-term exam is the day after tomorrow. . . . This is definitely a very painful but ineffective way (I personally used to do it often when I was in school, so I know it well). The author believes that stress is one of the main reasons that the brain cannot function properly, and to reduce stress, it is necessary to " start early ". Break up your long-term and mid-term goals (e.g., passing or getting a high score) into many smaller pieces that you can accomplish each day .

... Please convert distant deadlines into daily work goals, and complete them bit by bit.

In this way, in addition to reducing stress, you can also have enough time to increase the number of "recovery memory" and "self-test", and improve the degree of utilization and memory depth.

(2) Summarize ten good reading methods:

At the end of the book, the author summarizes ten good reading methods with many benefits:

1. Recall the learning content: After learning a paragraph, close any textbook, think about what you have just learned, and whether you can say it again or deduce it in your own words. In addition, frequent trips to different environments (for example: on the way to the bus, for a walk or jog, or while taking a shower) for retrospective review can not only reduce stress, but also improve on-the-spot performance.

2. Test yourself: that is, "consciously" test yourself. Find similar questions anytime, anywhere, or use flashcards to test yourself.

3. Create question chunks : "Chunks" are a knowledge-structuring metaphor often mentioned by authors. In the author's words:

...chunks are groups of information that are grouped together in meaning.

Meaning is very important here, and again we appreciate the "deliberate" part of the author's emphasis. For example: even if a person has "image memory" and can completely memorize a 500-page or one-hour speech by listening to and reading it once, if it is quantum physics content that is completely irrelevant to his English literature major, then even if He remembered it completely, and it didn't make sense to him, and it couldn't form chunks.

The "problem chunking" rule is to hope that readers can fully understand the solution of the problem into each part. On the one hand, the next time you encounter the same problem, you can quickly solve it; on the other hand, the knowledge internalized through the problem block will have a greater chance to be used.

4. Spaced practice : separate the arrangement of study and review. Brain training is like muscle training, which cannot be maintained at a high intensity for a long time. Meetings can only be fully developed under appropriate and stress-free circumstances. So it's best to start early and break down the ultimate learning goal into small chunks that you can easily accomplish every day.

5. Practice different problem-solving skills alternately: The author mentioned two points in this part: First, don’t use only one method to solve math problems (there are more than 200 methods to prove the “Pythagorean Theorem”) Second, find When you make a mistake, make sure to "make sure you know 'why' you're wrong" and "how is the right solution" (of course, every step of the solution has to be understood).

6. Rest: not just eating, sleeping, and playing electric games. Walking and fitness exercises are also very effective. In other words, let divergent thinking "diverge for a while."

7. Use explanatory questioning and simple analogies: This is actually another recommended learning strategy in the book: the Feynman technique. There are two main points in this method: First, can the knowledge or skills learned be explained in a way that "easy to understand even a 10-year-old child"? Second, compare concepts in the field of knowledge with things that are common in one's own life. In addition, the author also emphasizes again: don't just do it in your head, try to say it out loud or write it down with pen and paper. The author says:

Almost every concept you learn can find an analogy in some aspect of knowledge you already have. Some classes or metaphors can be crude, such as blood vessels as highways, or nuclear reactions as falling dominoes one after another. But these simple analogies and metaphors are powerful tools that help you build on existing neural structures and allow you to build new and more complex neural structures more quickly.

8. Focus : Turn off your phone, computer, iPad, or Macbook (and preferably if you have an Apple Watch), and focus your mind and time in mindful thinking only on the things you want to learn.

9. Eat the frog first: The so-called frog is used as an analogy to "the part of my heart that I hate but have to learn". Originally from career coach Daphne Gray-Grant's advice to clients:

... "If you have to eat frogs, eat them early in the morning." Wake up in the morning and do your most important and most annoying job; it's surprisingly effective.

Meaning: Make your least favorite or most difficult part the first thing you do when you wake up in the morning and feel refreshed. The rest of the rest of the day will be easy and less stressful because the worst part is no worse than "that frog" after getting out of bed.

10. Use psychological contrasts : This is actually a matter of "belief". The author asks readers to think about the past and what they want to be in order to come. In this way, it can achieve the motivational effect of giving self-confidence.

Finally, we use the book's "building meaningful chunks" to memorize these ten good reading methods. The first letters of the English words of these ten methods are: R, T, C, I, S, E, F, F, C. At first glance it seems confusing and meaningless, so I'm going to rearrange them into "meaningful chunks". F,I,R,S,T can be spelled into the word "first", and can be understood as "the first", "the most important" (so the first priority), as for CFCE, you can find it from Google. The abbreviation of a computer science certification is just "CFCE", which is "CERTIFIED FORENSIC COMPUTER EXAMINER". Because I also like to learn to write programs, I think this abbreviation is suitable for me to remember. So I compiled these ten points into "CFCE first!" (CFCEfirst) to memorize.

Inevitably, I still disagree with some of the points in this book. The larger ones are as follows:

1. Too many daily studies or work are scheduled:

The author believes that planning what to do or study progress the next day before going to bed is quite helpful for the development of brain activity the next day. However, the author goes so far as to think that the to-do list can be as many as twenty items!

... make a work list before bed, and you can summon the zombies in your head to help you with the next day's tasks. ...write down up to twenty to-do items. Every night, create a schedule for the next day based on the to-do list for the week, and limit your daily servings to five to ten items.

This is very different from what similar guide books I have read in the past. Generally speaking, because people's physical strength, willpower, and attention span are limited, there are trade-offs that must be made to get things done rather than just done. If there are twenty items in a day, each item can be allocated less than 30 minutes of time.

From my past reading experience and listening to the key recording of the book "Essentialism: How to Cope with Overcrowded Work and Life" (hereinafter referred to as " Essentialism ")): Highly productive people usually only schedule one day. Enter three to five important tasks; the first three are "must be done on the day", and the first priority is "must be done on the day". For the others after the fifth pick, it depends on whether there is time on the day. I recommend that readers listen to the key recordings of the book "Essentialism" and compare it with the author's point of view.

2. The benefit of frequently changing the learning environment is debatable:

The author confirms as:

... make a work list before bed, and you can summon the zombies in your head to help you with the next day's tasks. ...write down up to twenty to-do items. Every night, create a schedule for the next day based on the to-do list for the week, and limit your daily servings to five to ten items.

The “zombie” above actually refers to the automatic mode after people form a habit; they can do well without taking a test; for example: brushing teeth and washing face after getting up in the morning, driving the same road to get off work every day, etc.

It also differs from my past reading experience.

In the book "Habit Power: Breaking the Myth of Willpower, the Extraordinary Power to Change Your Life Unconsciously" (hereinafter referred to as " Habit Power "), he particularly emphasizes the importance of "environmental cues" in the process of forming habits.

The medical profession often advocates: do not do other things in the bedroom (for example: reading, playing electric games, etc.), because it will destroy the quality of sleep. why? That is because if we do something in the bedroom space for a long time, whenever we enter the bedroom, we will unconsciously want to read or play video games, which will crowd out or negatively affect good sleep.

Conversely, if we always read books at a certain location in our home, or always choose a quiet corner of a coffee shop to write, our bodies will get used to doing the same activities as soon as we arrive at that location; perhaps studying exam materials, Maybe review your own photography and document it. In short, in the process of forming a habit, a fixed environment can provide cues for automatic behavior, allowing us to reduce the obstacles to consider whether to do or how to do it after we arrive at the place.

Therefore, I have reservations about this part, and I ask readers to review after reading books such as "The Force of Habit ".

Overall, I highly recommend the book "Use the Right Brain, Never Be Afraid of Numbers". In addition to having a real strong proof and convincing from a literature student/mathematical losers to a Ph.D. in the School of Engineering, the book also clearly and simply explains the various connections between learning and brain activity (to give full play to The spirit of the Feynman method of learning). In addition, at the end of each chapter, there are "key sorting" and "successful case introduction" (mostly real stories of scumbags who have successfully counterattacked into academic bullies), and highly actionable methods are proposed for various suggestions. I sincerely recommend that you read this book.

The above is my comment on "Use the right brain, no longer afraid of numbers: learn how to learn, and how to think creatively, to solve (almost) all problems" (Second edition title: "The brain likes to learn: first know your own brain, find With the right thinking path, you can focus, not procrastinate, improve your memory, and learn how to learn” ). May good books help you and I grow together.

Book Information:

"The brain likes to learn this way: first know your own brain, find the correct way of thinking, you can focus without procrastinating, improve your memory, and learn how to learn"

"Deliberate practice: a comprehensive analysis of the original creator, a learning method more critical than talent"

Essentialism: How to Cope with Overcrowded Work and Life

"Habit Power: Destroying the Myth of Willpower and Unknowingly Changing Your Life"

More good book reviews are welcome

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