In the new era, what kind of learning ability do we need?

Bacon once said: Knowledge is power. However, only understood knowledge is power, and only those who are good at thinking are creative. Today, the advancement of science and technology and the development of artificial intelligence have put forward new requirements for human intelligence. In the old days, people respected those who had profound knowledge, but in modern times, only those who can deeply understand and create human knowledge are truly people with outstanding minds. This article provides a method and idea to achieve this goal. Although it seems to study the issues of "teaching" and "learning", its readers are not limited to students and teachers. It should be said that it is more suitable for scientists, social science researchers and leaders, or people who think about problems like these people.

I wish all readers of Fanpu a better mind and healthier body in the new year!

Written by Wu Jinshan (Professor at the School of Systems Science, Beijing Normal University)

Everyone knows that learning requires methods, but no one knows what the specific methods are. A lazy or helpless answer is: there is no fixed rule. We see that many students who study well do not spend most of their time on studying. I was such a person when I was a student. However, when we think about, or are asked, what learning method has enabled us to achieve this effect, we usually can't explain it. I remember that the answer I gave myself was to think more, think freely, and think without restrictions. Although I now know that this answer actually makes sense (this reason will be explained in this article using concept map comprehension learning), it is hard to say how much the listener and questioner can understand from this answer. We also have some such experiences or experiences: when some people are familiar with a field to a certain extent, they can "inspire" or "think carefully" to establish connections between this field and other fields; there are also people who can propose and solve very profound and difficult problems, and often such problem-solving methods can become the basis for solving other problems rather than just the original problems. We often call such people very creative. If we ask such people what improves their creativity, not many can give a good answer. I am one of them. I often connect things from different fields and often think about one or two of the most profound questions in a subject, although I have not yet answered many of them. If you ask me, and I have been asked this question before, my answer is basically to think more, think freely, and think without restrictions. Tang Chao, a physicist who can be considered to have achieved some success and one of the original creators of the sand pile model[1], was also asked this question. After thinking for a few minutes, he jokingly answered that he should read more, think more, and talk more. Although I now know that this answer makes sense, only a few people, including the listener and the questioner, can gain true knowledge from it. Therefore, efficient learning and thinking require and have methods. Everyone understands and agrees with this principle. However, no one knows what the method is.

Efficient teaching is also necessary and has methods. Teaching is to enable students to learn to learn and think. Since learning and thinking require and have methods, teaching naturally requires and has methods. However, this problem is more difficult than the former, and there are fewer methods available for reference. We have probably all heard that "teaching is an art". Any art means that there are few things that can be generalized and programmed, and many things that are personalized. Many famous teachers, such as Richard Feynman, the author of the Feynman Physics Lectures and a genius physicist, Leonard Susskind, one of the founders of superstring theory and the main lecturer of a series of theoretical physics open courses at Stanford University, Michael Sandel, the main lecturer of the "Justice" open course at Harvard University, and Ben Polak, the main lecturer of the "Game Theory" open course at Yale University, are not from education backgrounds, but from their own research work and research fields. Well, in this case, do we have some methods to improve the efficiency of teaching? Yes, but there are very few general methods. However, the concept map teaching method we are about to introduce is one.

The big picture of disciplines

The concept map comprehension learning we are going to introduce here is an effective learning and teaching method proposed from the research at the level of "low-energy approximation" - "low-energy approximation" is not very nice, so we give it a name, phenomenological research, which is basically based on phenomena, and the basic principles are not very clear - research. In addition to this goal of improving the efficiency of learning and teaching, more specifically, what problems does this method mainly solve? Solve the problems of what to learn, how to learn, what to teach, and how to teach. Don't think that the problem of what to learn and what to teach is a mediocre problem . Of course, if you think that everything should be learned and taught, and students should learn as much as possible, then you are not the reader of this article. The total time of students is limited, and the time for learning cultural knowledge should be even more limited. Students also need to spend a large part of their time to contact different things, understand and appreciate nature, make friends, be in a daze, climb trees, go fishing, play games, exercise, spend family time with their families, and so on. Spending time on any unworthy book, a class that is not worth taking, or a knowledge point that is not worth learning means reducing the time that could have been used to increase life experience and life fun. Especially for us teachers, every time we don't choose the most appropriate content to teach, we force students to waste time with us, and a lot of students have to waste time with us. Therefore, it is necessary for teachers to carefully examine the necessity and rationality of each teaching content. Of course, if you are the kind of teacher who just picks up a book and teaches, and does not actively think about what to teach now, and does not plan to think about it in the future, then you are not the reader of this article.

So, what should we learn and teach? Let me give you an example that is not quite appropriate, and because it is not appropriate, it is more profound. Many parents teach their children to calculate addition and subtraction when they are very young. Many children's understanding of addition and subtraction is based on memory, and they do not understand the meaning of addition and subtraction. In other words, at the beginning, children do not know that 1 + 1 = 2 means "one unit of something plus another unit of the same thing is two units of the same thing", but they can already answer the questions asked by adults, "So-and-so, what is 1 + 1?" Some parents are secretly happy about this for many days. The conclusion I want to write down now is: if we only consider addition and subtraction itself, except for a certain amount of calculation practice in order to understand the meaning of addition and subtraction, children should never learn the calculation of addition and subtraction. For any addition and subtraction, as long as children can convert practical problems into addition and subtraction problems, the learning task is completed. Of course, in order to skillfully convert between practical problems and mathematical expressions, a certain amount of practice is necessary. However, mathematics is definitely not arithmetic operations, and these operations can be completely handed over to calculators. Similarly, students do not need to master or memorize all the calculus. They only need to learn how to transform practical problems into calculus expressions. After the transformation is completed, we have specialized tools such as SageMath[2] and Maple [3] to complete it. Therefore, it is time to stop learning arithmetic for the sake of arithmetic and calculus for the sake of calculus.

So, what should we learn and teach in mathematics? Do we need to be proficient in arithmetic and calculus operations? Yes, but for completely other reasons. Readers with a certain level of attainment in mathematics will understand that factorization is an important way of thinking, and many difficult problems can be made simpler with the idea of ​​factorization. To do factorization well, you need to have a good sense of addition, subtraction, multiplication and division of integers. Familiarity with arithmetic operations is to cultivate this sense. Variable substitution and modularization are very important in analyzing many complex problems. Sufficient training in calculus operations can give you a pair of sharp eyes, prompting you to make appropriate variable substitutions and modularize problems. So, these two inappropriate examples are very good and I like them very much. In other words, whether something is worth learning or teaching, in addition to considering the interests of students and teachers as individuals (we don’t care about this, some people just like to make an encyclopedia, like to challenge Wang Xiaoya, Li Yong, Chinese Character Heroes, I love to remember lyrics, this is their freedom. By the way, such people are not the readers of this article.), the most important thing is to see what other things can be used to understand or creatively apply this thing or solve what kind of problems, to see the position of this thing in the entire discipline, and what aspects of the discipline’s big picture it reflects . Of course, I am assuming here that the ultimate goal of our teaching is to cultivate people who explore the world, whether it is the human behavior or natural behavior of this world. Therefore, I imply that the object of cultivation I am talking about is actually people similar to scientists, social science researchers, and leaders, or people who think about problems like scientists, social science researchers, and leaders.

Back to our topic, at the level of subject teaching and school teaching, what to learn and what to teach is a big problem. So how do we determine what to learn and what to teach? We say that we need to look at the position of a content in the entire knowledge framework or the big picture of the subject. So how do we determine the position of a content in the entire knowledge framework or the big picture of the subject? We need to rely on concept maps. How to use concept maps to determine the position of a content in the entire knowledge framework or the big picture of the subject? We will discuss this in the future. Before that, we must see that with the advancement of technology, electronic terminals can be found everywhere, search engines are becoming more and more accurate, people's demand for memorized knowledge itself is getting less and less, and the demand for becoming a knowledgeable person is getting smaller and smaller. At the same time, the demand for creative use and creation of knowledge is getting higher and higher. Understanding knowledge is the basis for creative use and creation of knowledge . The content of our learning and teaching should focus less and less on questions that can be solved by simply asking Google [4] or Siri [5], and more on asking questions that have never been asked before, answering questions that have never been answered before, answering questions in new ways, providing new answers to a question, and focusing on how to promote the progress of human civilization.

So, what do we rely on to raise questions, solve problems, create knowledge, creatively apply knowledge, and understand knowledge? We rely on understanding and grasping the big picture of one or more disciplines. In other words, we rely on understanding and appreciating the typical thinking style and typical analysis methods of researchers in this discipline, and on understanding what typical objects researchers in this discipline study and what typical problems these typical objects have. After understanding the typical thinking style, typical analysis methods, typical objects, and typical problems, we can understand the relationship between this discipline and the world and other disciplines. So, one day when you face a related problem of a related object, you know how to express the problem as a problem of a related discipline, and try to solve the problem with the thinking style and analysis methods of the related discipline, and even develop new thinking styles and analysis methods by solving this problem.

For example, for physical problems, we usually ask: how to describe the state, whether the state will change, and if it does, what is the reason for the change; when we think about the reason for the change, we often think from the perspective of the interrelationship of things to see what things act on or affect this object; when we really write down the description of the state and the reason for the state change, we often use mathematical structures and mathematical equations; finally, generally speaking, the standard for judging whether our mathematical structures and mathematical equations are right or wrong is to examine a similar new phenomenon, use these mathematical structures and mathematical equations to calculate this phenomenon, see what happens, and then compare this "what happens" with the "what actually happens" obtained by actually doing an experiment and measuring this phenomenon. In more professional terms, these are called "mechanical worldview", "interaction", "equation of motion", "mathematical modeling", "experiment and measurement", and "verifiability". In addition to learning specific equations for certain phenomena and solving specific equations, learning physics also requires understanding these terms - they truly represent what physics is. This is the big picture of physics: generally speaking, we care about the natural part of the puzzle of this world, and most of the issues we focus on are how we use mathematical models and calculations to describe or solve this puzzle. The criterion for solving the puzzle is that the results we calculate and the experimental measurements are consistent within the error range. At the same time, most of these mathematical models are constructed from the perspective of analysis and synthesis from the perspective of the interaction between individuals.

After clarifying the big picture of the discipline, there are of course other typical analysis methods and typical ways of thinking for more specific problems, such as the role of symmetry in the mathematical model of the electromagnetic field, the impact of symmetry on the entire physics theory, the methodological significance of correlation functions and phase transitions in physics and beyond physics, etc. The next step is to find appropriate specific problems and specific knowledge as examples to demonstrate one or more items in the big picture of the discipline and promote learners' understanding of the big picture of the discipline. This is a two-way process: when learning each specific problem and specific knowledge, try to extract the big picture of the discipline that can help students understand; for each big picture of the discipline that you have extracted, find the most appropriate specific problem and specific knowledge as an example.

Figure: What is the big picture of a discipline: the typical research objects, typical research problems, typical ways of thinking, typical analysis methods of researchers in this discipline, and their relationship with the world and other disciplines.

In addition to the connection between specific knowledge, specific problems and the big picture of the discipline, another important connection is the connection between knowledge. Generally speaking, a relatively mature discipline will always find some basic concepts and basic assumptions, and then regard other concepts as these basic concepts and basic assumptions, and obtain other knowledge through general human logic or the typical thinking mode and analysis method of this discipline (of course, they also meet the constraints of general human logic and can be regarded as the specific manifestation of general human logic in this discipline). So, in the process of learning with the big picture of the discipline as the goal, we must also organize and use the connection between these concepts. Through the connection between these concepts, we may also better find out the key concepts and key knowledge that are much less than the concept set of the entire discipline to construct the knowledge of the entire discipline and experience the big picture of the entire discipline. This is the meaning of "connected thinking" in concept map understanding learning. Here, it needs to be emphasized that the big picture of the discipline and the minimum and most critical examples of specific knowledge and specific problems that have growth potential - growth through connection - to help learners experience the big picture of the discipline are the answers to what to learn and what to teach. In addition, concept map understanding learning is also part of what to learn and what to teach. The big picture of the subject, specific knowledge and learning methods learned in this way will also allow learners to feel the charm of the subject and form feelings for the subject. These are what should be taught and learned.

This kind of learning is completely different from the learning in the early days that aimed at profound knowledge. In that era, having the opportunity to learn knowledge, having knowledge to learn, and having formulas and memorized tables to look up in the future was already a great thing that only a few people could do.

Let me give you another example to illustrate the changes in learning content in the new era. Consider a trip you take. Your goal is to get from an area Z that you are familiar with to a place O that you are not familiar with. If there is no map, you need to consult experts who are familiar with both areas, or even all the areas that you may need to pass through in between, to develop a travel route. Moreover, you need to remember where the turns on this travel route are, either in your mind or on a piece of paper. Moreover, we cannot guarantee that the route obtained after consulting experts is the shortest or the most convenient to drive or walk. This travel mode without an overall map, relying only on local exploration by the traveler and expert guidance - such guidance also basically relies on memory-based knowledge, which is the most reliable travel plan before the popularization of GPS positioning technology. Now with maps and electronic maps, we no longer need pure knowledge experts who can remember these areas. What we need is timely updated road conditions and good path search algorithms, an "expert" who processes maps and traffic information. Of course, in fact, we found that except for those who specialize in such algorithms, ordinary people can even replace this algorithm with the computing core and the program running on their mobile phones. In other words, now, you only need a map, a positioning system, a path search algorithm, and then you go out. Basically, we don't need to remember anything. Of course, in the real world, we will encounter problems such as maps not updated, algorithms with bugs, and algorithms that may be slow. We cannot completely forget the way, and a small number of road signs may still need to be memorized.

The incident that happened to me and my child two days ago when we were looking for a toilet in a shopping mall can give us a deeper inspiration on learning methods. We needed to find a toilet in a completely unfamiliar shopping mall. First, we looked at the sign and didn't understand the instructions. Then, we asked for directions and learned that there was one in a corner, and we were given a specific route on how to "beat around the corner".

Unfortunately, the route was too complicated for me to remember. However, I remembered two things: there was a toilet on this floor, and it was in that direction. So, I set out with my child to look for the toilet. After turning many corners—and later realizing that we had taken a few detours—we found the toilet. In the matter of finding the toilet, it is enough to know and believe that there is a toilet within a certain range, and to know the general direction, without having to remember a specific route. When I found the toilet, I thought of learning: when learning, it is most important to understand and believe that something—such as a course or a book—has something worth learning, something you like to learn, or something that can solve your problems and satisfy your curiosity. Then, when learning, you must have a sense of direction—which can come from your own accumulation and intuition, or from the inspiration of teachers or classmates. It is this belief and sense of direction, rather than specific definitions and calculations—of course, when you really want to understand what you are learning, it is very important to have a deep understanding of these definitions and calculations [6]—that can basically ensure that you can understand and learn, even though you may have to take some detours.

The inspiration from the GPS example above is that as the times progress, our demand for pure memory-based knowledge will become lower and lower, while this example of finding a toilet tells us that belief and sense of direction are more important for learning and research work than specific knowledge. Of course, you will ask where such belief and sense of direction come from. If there are instructors and study groups, then this belief and sense of direction can come from such pioneers. However, since we emphasize self-study, then when we basically rely on ourselves to study, where do such belief and sense of direction come from? It comes from the understanding of one's own interests and abilities, and from the grasp of the overall big picture of the knowledge that has been learned. So, how to grasp the big picture from the specific knowledge learned? Let's discuss the question of how to learn and how to teach below.

Creating experiential learning

Now, let's complete the example of the mother showing her child 1 + 1. Learn from this how to learn. I have been ignorant and always tell the truth since I was a child. One day, a mother held her two-year-old child and proudly said that her child could calculate 1 + 1. Then, a group of people started to make a noise and asked her to demonstrate it. The mother asked the child, "Xie XX, what is 1 + 1?" The child answered "2". Then, the mother proudly turned around with the child in her arms and prepared to leave. At this time, I jumped out and asked, "Xie XX, do you know what 1 means, what 2 means, what + means, what = means?" Then, the child and the mother were embarrassed and left. I don't want everyone to be as ignorant as me, although I still tell the truth to this day. I just want to emphasize that if we want to understand the meaning of 1 + 1 = 2 - if we count one thing in a certain unit and get a quantity of 1, and count another thing in the "same unit" and get a quantity of 1, then we need some basics - understanding of counting and quantity, understanding of units and the convertibility of units and ensuring the same units (for example, a pair of socks and a pair of socks add up to two pairs, but a pair of socks and a sock are not easy to deal with), understanding of "addition is to count together", and understanding of the meaning of "the equal sign indicates that the quantity is equal, and the form is generally not exactly the same". Before establishing a preliminary understanding of these things, although it can be deepened in the future with further learning, we should not directly learn addition calculations. Such learning of addition calculations before understanding the above things can basically only become memorization, relying on memorization and repetition to learn, which is called "rote learning". So, if we don't consider the learning cost, is it true that mechanical learning that mainly relies on memory and repetition is actually not bad, and can it also become one of the main methods of learning and teaching? No. Because from mechanical learning, we cannot learn the big picture of the subject.

Let's go back to what to learn and what to teach. We have said that the fundamental purpose of learning is to raise questions and solve problems, to understand the world, and to make the world a better place. Of course, most of the problems to be solved are problems that have been encountered by others before, so you only need to have a database of how others have solved this problem, find out how the predecessors solved it, and then copy or slightly modify it to solve the problem you are facing. However, the fundamental of scientific progress and social development is to raise and solve new problems. When you face a problem that no one else has ever solved, what is more important is no longer the database of answers, but the typical thinking methods and typical analysis methods that predecessors have extracted in the process of solving related problems. Even the experience and insights of predecessors when raising questions may help you raise new questions. And these cannot be accomplished by repetition, memorization, and table lookup. This is why we must deny mechanical learning.

Of course, denying mechanical learning does not mean that learners do not need or cannot use the tool of memory. First of all, some things that require high skills can only be learned after a certain amount of practice. For example, in addition to understanding the principles, practicing music even requires the formation of muscle memory.

Secondly, for some knowledge, memory and understanding can promote each other. Remembering something helps to react faster, making it easier to establish connections and promote understanding; at the same time, some things can be remembered more efficiently after understanding. For example, after understanding the relationship between a character and its components (for example, one component may represent the meaning and another part may represent the pronunciation), you can better remember and use the Chinese character. Finally, sometimes after understanding and connecting, you can summarize some formulas to help solve problems more quickly, which is not impossible. For example, by calculating the addition of single-digit numbers many times, you no longer need to count your fingers to calculate the addition, but actually form an addition table in your mind. For example, by calculating the multiplication of single-digit numbers many times, you do not need to convert multiplication - repeated addition - into addition every time to calculate, but form a multiplication table in your mind to calculate. These are all places where memory as a learning method can play a role. What we oppose is to directly teach and learn by taking the memory of knowledge and the memory of formulas as the goal and means of learning. Let learners experience the process, even pain and joy, of asking questions, solving problems, and establishing connections to understand the problem and solution. Then, it is best to form memories through their own organization and summary. This kind of memory-based learning can be achieved.

Speaking of mechanical learning, I would like to share an example. Influenced by the trend of "massive reading" and "classic reading", I have recently seen questions in the form of "main content of classics" in the Chinese language questions of the middle school entrance examination and the college entrance examination. For example, asking which main characters are in "Twenty Thousand Leagues Under the Sea" and what happened between them, asking who are the main characters in the "Empty City Plan" in "Romance of the Three Kingdoms" and what happened, asking what are the main writing characteristics of a certain book, and so on. Of course, the original intention of these questions is to stimulate children to read classics. However, as long as the questions are asked in this way, then, in the future, there will naturally be learning reference books of the type of "famous book guide" and "famous book reading". These books will make a concise summary of the main content and writing characteristics of the classics within the scope of the exam. Students only need to memorize these summaries to get high scores in such exams. Therefore, it is still impossible to encourage students to really read classics by themselves. Mechanical learning is a shortcut to improve grades in the short term, and it is an obstacle to truly learning the big picture of the subject in the long term. So, back to the study of Chinese, why do we want students to read classics? Is it to improve reading and writing skills, especially the reading and writing of written language and slightly abstract topics? If so, then can we not use the test questions about "the main content and writing characteristics of famous works" to test whether the learning effect has been achieved? In this way, in the teaching and learning of Chinese, we can also not rely on pure repetition and memorization learning such as "famous works introduction", "famous works reading on behalf of others", "refined summary", etc.?

Back to our topic, then, when we deny mechanical learning, how do we learn? Here we still use the example of travel planning to discuss this issue, but here we use its abstract meaning and analogical meaning, rather than real travel. Suppose, your learning goal is the unfamiliar concept O that you want to reach. Now, you need to start from the familiar field Z and learn O. What to do? If we have a map, a map about the relationship between these concepts, we can start from Z and learn O through the connection between concepts. Similarly, if we are faced with a proof question, the goal to be proved is O, and the starting point is the known theorems, axioms and definitions in area Z, then we need to build a path from Z to O. At this time, a map that includes knowledge of Z and O and most of the intermediate concepts will play a very important role and greatly improve our learning and thinking efficiency. Just like the importance of actual maps when we make travel plans, for understanding concepts, applying knowledge and creating knowledge, concept maps are maps in our cognitive structure. Therefore, how to teach and how to learn still depends on this map. At this time, if we establish a new connection between the two existing concepts, it is actually equivalent to building a new road. Looking at the significance of a new road on an actual map for the entire traffic, you can appreciate the value of such a new connection in the cognitive structure. At this time, the concept map can also prompt you where to build and how to build such a new road. This is what we mentioned at the end of the previous section: the content of our teaching and learning is to use the minimum and most core concepts and research examples and the connection between them to let learners understand the big picture of the discipline, and the method used is to focus on the connection between concepts, research work, and the big picture of the discipline, so that learners can build the concept map of the knowledge they have learned to experience the big picture of the discipline. And in such a connection, we must pay attention to the internal connection, rather than the far-fetched connection. This focus on the internal connection rather than the far-fetched connection, I will share an example later, is part of critical thinking. Therefore, in summary, how to learn and teach depends on "understanding learning guided by critical thinking and associative thinking with the big picture of the discipline and the growth-oriented thinking goals and based on the concept map as the technical basis."

At the same time, this concept map can be used to reflect the cognitive structure of the concept map maker. Therefore, the process of making a concept map also plays an important role in discovering problems in learning and understanding and formulating targeted and personalized learning plans. Therefore, concept maps can also be used for evaluation and diagnosis of teaching and learning. Due to the function of concept maps in reflecting the maker's thinking and understanding, the use of concept maps in teaching can achieve personalized teaching to a certain extent. David Ausubel said in his "Educational Psychology":

If I had to reduce all of educational psychology to just one principle, I would say this: The most important single factor influencing learning is what the learner already knows. Ascertain this and teach him accordingly.

If I had to summarize the principles of educational psychology in one sentence, I would say: The most important factor affecting learning is what the learner already knows. Teach after you have understood and considered these things.

Therefore, the question of how to learn and how to teach is a matter of two maps: the first is the concept map of the core knowledge of the subject - the concept map of the concept relationship of the subject is objective, but the concept map made by the subject experts or lecturers is always an approximation of this objective relationship with the subjective color of the maker; the second is the concept map of the students' existing relevant knowledge - this reflects the students' grasp of the concept relationship of the subject during the learning stage. Moreover, the latter needs to be constantly updated in the learning process.

In the process of constructing this two-concept map, in addition to paying attention to the connection between disciplinary concepts, we also need to pay attention to the connection between concepts and the disciplinary big picture, that is, try to choose those concepts that can reflect the disciplinary big picture and the connection between concepts as the content to be learned and understood. This is the learning method we proposed [7] and advocate: understanding learning with the disciplinary big picture and growth-oriented thinking as the goal, critical thinking and relational thinking as the guidance, and concept maps as the technology.

Note: This article is authorized to be selected from Wu Jinshan: Teach Less, Learn More: Concept Maps for Understanding Learning (Science Press, July 2021). Due to space limitations and other reasons, it was slightly edited when it was published in Fanpu. The title of this article was added by the editor. Interested readers can go to Professor Wu Jinshan’s personal WeChat public account to learn more about it.

Notes

[1] Many people say that Tang Chao’s mentor, Per Bak, who is also one of the original creators of the sandpile model, is a man of extraordinary creativity. Unfortunately, I cannot hear Per Bak’s answer to this question. If you want to learn more about this man of extraordinary creativity, you can read Per Bak’s book How Nature Works: The Science of Self-Organized Criticality.

[2] SageMath is a mathematical software that can perform symbolic and numerical calculations. Sage: Open Source Mathematics Software, http://www.sagemath.org/, accessed on April 20, 2017.

[3] Maple is a mathematical software that can perform symbolic calculations. The Maple Software, http://www.maplesoft.com/, accessed on April 20, 2017.

[4] Google is a search engine, http://www.google.com/.

[5] Siri is a voice control system that can answer some of the user’s questions by automatically searching the Internet and information.
https://www.apple.com/hk/en/ios/siri/.

[6] For a discussion on the understanding of specific definitions and calculations, see Wu Jinshan's "Teaching less, learning more - Concept Maps for Understanding Learning" Section 10.17, "Qin Lei, Wu Jinshan: A dialogue on the relationship between mathematics and scientific theories and reality and learning methods."

[7] It cannot be said that it was entirely proposed by us. Independently, each part of which is based on the independent view, "growth thinking", "concept map", "discipline picture", "critical thinking", "connective thinking", and "understanding learning" were all proposed before us. However, as far as I know, we should propose it.