Silas's understanding of knowledge is shallow and loose, and even slight changes will make him at a loss. This is because he understood his study as memorizing a bunch of isolated facts, but did not thoroughly understand the connotation of concepts and the relationship between them.
No matter what you learn, please understand it deeply and make your knowledge rock solid. If you are learning a piano piece, please don't just memorize the movements of your fingers, but learn to listen to every note and understand the structure of the whole piece. Ask yourself:? Can I hum the notes of my left hand and play the music of my right hand at the same time? ? If you are studying the American Civil War, please don't just remember some key points. Lincoln is the president, Lee is the general, and slavery is very important. You can try to understand the background that triggered the bloody conflict, the accumulated hostile forces and the changing social values. Or when you want to make a political decision, please don't just focus on the appearance of the candidate and the 15 second speech clip. You can objectively understand the relevant events and form your own well-founded views on this basis.
You can understand anything more deeply than you do now. ? Do you understand? What is this? Set a higher standard for yourself? Do you understand? Can completely change your perception of the world! The steps listed below will explain why a deep understanding is essential to consolidate future thinking and learning.
Start with a deep understanding of simple knowledge.
The most basic concepts in any subject can be understood continuously and deeply. Professional tennis players will pay attention to the trajectory of the ball, mathematicians will understand the nuances of the concept of numbers, good students will continue to deepen their understanding of the concepts learned in the previous chapter or course when studying advanced chapters or courses, and successful people will habitually pay attention to the core goals of their careers or lives. All real experts will constantly deepen their mastery of basic knowledge.
Tony? Plog is an internationally renowned trumpet player, composer and teacher. A few years ago, we had the opportunity to witness him give advanced training courses to several excellent soloists. In that class, each student performed a famous music of his own choice. Their performance was wonderful. Tony listened politely, and then commented from time to time: Good, good. This job is very challenging, isn't it? ? Then, as always, I began to give suggestions to the students, such as how to play this song better, how to play the body skills, and how to feel the music. Nothing special.
But then he changed the subject. He asked the students to play a very simple etude, which any trumpet beginner can play. So they played these extremely simple notes, which sounded rather childish and clumsy compared with the extremely fast notes in the complex movement at the beginning. Tony picked up the trumpet in class for the first time after all the students played this simple piece. He also played the same etudes, but his performance was not naive. On the contrary, it is quite elegant, and every note is full of joy.
He gave this piece a beautiful timbre, and the sense of movement made us realize the meaning contained in these simple notes. The students are far behind. This contrast is shocking. The fundamental difference between a real master and a gifted student obviously occurs at the most basic level, not in complicated music. Tony explained that being able to play simple music incisively and meticulously can help players show higher control and artistic skills when playing extremely complex music.
The experience of this class is very simple. This master teacher intends to show that high-level students should spend more time practicing simple music and learn to play beauty and elegance on simple songs with advanced technology. Working hard on simple and basic things will help to create truly exquisite skills, not only in music art, but also in other fields.
What is a profound understanding? How can I realize that my understanding of something is not deep enough? When those high-level students played that simple little song, they played every note carefully and were very good to themselves. They may never realize that such a simple tune can be played so beautifully before hearing the real master play and feeling the strong contrast.
Do anything, please constantly improve the knowledge and skills related to basic concepts and simple cases. Once is not enough. Every time you revisit, you will find something new. Although returning to nature seems to be a retrogression, it still needs extra time and energy; However, if you build your knowledge on a solid foundation, you will soon feel that your potential will be better.
Ways to stimulate effective thinking
Master the basics. Think of a skill you want to improve or a subject you want to deepen your understanding. Take 5 minutes to write down the most basic elements of this skill or discipline. List all the concepts that follow. Now choose one item from this list and spend another 30 minutes actively deepening your understanding of this concept. Experience how to hone and deepen the basic knowledge into high-level skills and knowledge, and apply this exercise to all other knowledge you already know and want to know.
Example: How do students understand basic economics?
The first step is to discuss a series of concepts collectively. Profit maximization, free market, supply and demand, supply and demand balance. Please note that the list of students is neither coherent nor complete, which is good.
The second step is to improve, right Supply and demand balance? Understand. First of all, I need to understand the meaning of the supply-demand curve. The horizontal axis represents quantity and the vertical axis represents price; So I understand why the demand curve gradually drops to the right and the supply curve gradually rises to the right. I think the balance of supply and demand should be the intersection of these two curves, but if the quantity level is on the left side of the intersection, the price of demand is higher than the price of supply. I don't know what that means. Please note that this student successfully found that he didn't understand a basic concept, that is, what the supply-demand curve represents. Now he knows what he has to do first. A solid understanding of the basic concepts will help him go faster and further in the future.
Casting the core with common sense. Many of the most complex, subtle and profound ideas in the scientific community come from the observation of simple daily life, but this observation is often clear and unambiguous. Calculus is one of the most influential concepts in history, which has completely changed our way of life today, from space exploration to plasma TV, computer and mobile phone. None of this would exist without calculus. Calculus is based on deep thinking about simple and ordinary events, such as apples falling from trees.
1655, a black death swept across Britain. Cambridge University was closed for fear of the spread of this terrible disease, so Isaac? Newton and other students were sent home. Newton spent the next two years on his aunt's farm, during which he established the basic ideas of calculus and the laws of physics. The famous story of Newton sitting under an apple tree and being hit by an apple leads to the theory of gravity and calculus, which can be almost literally understood as true. Thinking about the speed of apple falling can produce the concept of derivative, that is, speed is a profound extension of the simple concept of distance divided by time. If we know the speed of every moment in the process of apple falling and find out the falling distance, we can introduce the concept of integral, that is, the concept that distance is equal to speed multiplied by time.
The greatest theories of the universe, such as the theory of celestial bodies, all come from deep thinking about the phenomenon that an apple hits Newton's head. Newton described the vast universe, the sun, planets and distant stars with laws describing ordinary things, such as apples falling from trees. Simple and familiar appearance actually hides complex and unknown mysteries! The depth of the basic knowledge you have mastered will affect your understanding of everything you have learned in the future.
Today, the math teacher was asked why calculus is so difficult to teach, and most teachers replied:? The students didn't fully understand the basic mathematical concepts they learned in Grade 8 and Grade 9. ? One secret of mastering calculus is to really master basic algebra. During the study of any course, when you prepare for the next exam, please make sure that you understand all the previous exams 100%. If not, you are not ready for the next exam. Teachers should also pay attention to this basic fact and help students have a deep understanding of the basic knowledge before exploring new knowledge.
If you want to learn any subject well and create a theory that transcends predecessors, you need to return to the foundation constantly. When you look back after learning a complex topic, the basic knowledge is much simpler than before; These simple foundations are also changing. The more you learn, the simpler the basic knowledge is, but at the same time, it is more subtle, deeper, more detailed and more meaningful. Just as a trumpeter master can find infinite beauty in simple etudes, he can also gain a deep understanding in more interesting and complicated movements.
Ways to stimulate effective thinking
Q: What do you understand? Do you really understand or not understand the basic knowledge? Imagine a topic that you think you know or that you are trying to master. Create a new blank document on the computer, and write down a detailed outline of the basic knowledge of the topic without referring to external information. Can you write a clear, accurate and comprehensive description, or is there a loophole in your knowledge? Do you have any difficulty in citing key examples? Have you ignored the overall framework of these knowledge modules? Now please compare what you have worked so hard to write with the material obtained from external resources (articles, networks, experts, bosses).
If you find yourself lacking in these basic knowledge, please take immediate action. Learn these basic knowledge in an orderly way, and thoroughly understand the knowledge points that you just added and the related knowledge points that you lack. Make this new knowledge a part of your basic knowledge and connect it with what you already know. When learning more advanced content related to this topic, please repeat these exercises at any time (and record your previous attempts so that you can look back and see how much you have improved). Every time you go back to nature, you will deepen your understanding of the whole topic.
How well do you know the candidates in the election, their past and their position? List the issues that are important to you. Then give each candidate a subjective score for each topic, such as their stated views, support rate and other issues related to this topic. Most voters don't know the candidates accurately or fully, especially those they don't support. Please refer to the factual records related to the candidates and examine the specific differences between them. Enriching your knowledge can help you make more informed decisions, both on election day and in the years to come.
Don't do it in the face of difficult challenges! 1961in an impassioned speech in the us congress on may 25, John? Kennedy inspired the people of the whole country with this sentence: I believe this nation should devote itself to the goal of landing on the moon and returning safely within ten years. ? On May 26th, the National Aeronautics and Space Administration (NASA) did not choose an astronaut. Instead, their first goal was to hit the moon. Three years later, NASA successfully made? Rover 7? Hit the surface of the moon at an impact speed of 58,665,438+0 miles per hour (this unmanned probe sent back more than 4,000 images of the surface of the moon to the earth). After continuous progress 15 repetitions, there is 1969 July 16? Apollo 1 1? Smooth landing on the moon and what followed? One small step for the individual, one giant leap for mankind? .
Great scientists, creative thinkers and problem solvers will not directly solve difficult problems. When faced with a difficult problem, they will give up immediately and wisely. They understand that it is better to solve simple problems efficiently than to waste energy on complex problems in vain. Solving simple problems can teach them how to deal with upcoming complex problems.
When in trouble, creative problem solvers will create a simpler and easier problem that they can solve. They thoroughly solve the easier problems first, and then pay attention to the rest. And these understandings usually point to the solution of the original problem.
Apply this mode of thinking to work: when faced with thorny problems or challenges, try to do something else first. Fully concentrate on solving sub-problems that you know you can solve successfully. Have full confidence in your in-depth and meticulous work on the sub-problem, which will lead you to solve the bigger and more complicated main problem, but please don't jump to the more complicated next step while you are still dealing with the sub-problem. First, just hit the moon and walk on it. That was another day.
Ways to stimulate effective thinking
Work on the details. Think about a complicated problem in study and life. Don't deal with the whole thing, but find out its tiny part and solve that part completely. Understand this sub-problem and its solution from beginning to end. Understand all its connections and meanings. Think carefully about this little problem from many angles. The selected sub-questions should be detailed enough to pay attention to the complete situation of the level where the problem is located. Then you should think about how to solve bigger problems.
Clarify the confusion and dig the essence
For a long time in the past, whenever flying was mentioned, people would think of birds. Whenever we think of birds flying, what floats before our eyes is the flapping wings of birds. However, anyone who has been on an airplane can now prove that flapping wings is not the essence of flying. What really works is that the air flows faster above the gentle arc at the top of the wing, thus generating a lifting force. This arc is the essence of bird flight and plane take-off. But it is difficult for people to see that flapping wings is a useless feature, because it is the most striking, ostentatious and obvious feature of birds in flight. We need to make great efforts to ignore the obvious flapping characteristics and find the imperceptible wing curve, which is not easy, but it is the essence that enables us to fly finally.
Uncover the essence. When you encounter a complex and multifaceted problem, please try to separate the most fundamental elements. It is not enough to find out the essence, but also to further understand how other features in the situation are embedded with the essential features to form the whole problem; Clearly identifying and separating the necessary elements can guide you out of confusion. The strategy of cleaning up the chaos and excavating the essence includes two steps:
Step 1: Identify and ignore all interference features and separate the core content of the problem.
Step 2: Analyze this core problem and apply these understandings to a larger overall problem.
Desperately looking for Willie. Martin? Hanford wrote a set of children's picture books, Where is Willie? Every page in the book has a big picture, and hundreds of small cartoon characters are intertwined. One of the characters is Willie, wearing a unique red and white striped shirt and a pair of round-rimmed glasses. If there were not hundreds of other characters on the same page, Willie would be easy to find. But children like to look for Willie in messy pictures. If all the non-Willie characters are removed, it will be easy (but boring) to find Willie. The challenge comes from clutter. Imagine that when you clean your desk, just throw away those messy things and the rest will be easy to find. Clarifying the chaos can not only reveal what you know already exists, but also reveal the essence of the status quo. Without this step, the essence is hard to detect.
The real problems are often surrounded and covered by history, background and decoration. In this fog of fuzzy connection and intertwined influence, you need to grasp the core. Usually you will be surprised to find that when you reduce a complex problem to its essential problems, these essential problems are so clear and easy to deal with. But it's hard to ignore everything. Usually the chaos around you is always flashing and making noise, frantically trying to draw your attention from the real problem. Only by systematically ignoring one interference after another can you turn your attention to more important (usually undetectable at first) topics. After clearing up the confusion, the rest will clear your understanding and open up new ideas. Remember, you may not see everything clearly, but at least you can definitely eliminate most of your distractions.
Picasso's masterpiece The Bull. 1945 rpm 1946, Pablo? Picasso created the bull series (figure 1- 1). If arranged according to the degree of detail, then the one with the clearest detail is the true portrayal of the bull image, and all the characteristics of the bull are fully displayed. In the next 18 series of paintings, Picasso simplified the original painting step by step. The shadow of the bull's fur disappeared, the details of the muscles disappeared, the texture was taken away, and the three-dimensional sense was gone. On the eighteenth bull picture, we saw a stick figure with ten curves and two ellipses. But it is these twelve symbols that extract the essential characteristics, strength and masculinity of the bull. Clear up the chaos and leave the essence. Only the last painting in that series was named bull by Picasso. By systematically excluding the minor parts (please be careful not to turn bulls into cows), we can force ourselves to see what is most important.
Ways to stimulate effective thinking
Reveal the essence. Think about a topic you want to understand, and clean up the confusing information until a necessary element is separated. Every complex problem may contain multiple core concepts. Keep the change, right? That? The most essential concept, just find an essential concept. Try to start with a theme and reduce it to a specific theme. In fact, you can apply this exercise to yourself. What do you think is your most important characteristic? Separating these characteristics can help you make life choices more clearly.
In the process of raising children, parents need to make many decisions every day. It is obviously unrealistic to seek advice from others every time you encounter a new situation. In fact, you can just set one or two basic goals and then use them to guide your actions. For example, one goal can be to train children to be independent thinkers and dare to take responsibility for personal life choices. This goal will affect your decision.
If your child fails to finish his homework many times, are you willing to accept a relatively simple and short-term effective scheme that can help the child finish his homework, or choose a relatively difficult scheme that encourages the child to learn independently? Keeping basic goals in mind can make daily decisions clearer. Whether you are a parent or not, similar thinking can help everyone-teachers, students, businessmen and even politicians-point their daily decisions to long-term goals, rather than short-term goals that will only distract you.
Once you separate the essence, you arm yourself with a solid core on which you can build and decorate. The core is not everything, but it can guide you through the storms of life like the North Star. What is the essence? What is fur? Find out the essence of the problem, and start from there, and you can show yourself confidently.