Now, let's begin to apply the ideas I expounded in the previous part of my speech (3 1 page). The initial cycle of infancy is very successful, followed by the cycle of adolescence, starting from the most romantic stage we have experienced so far. It is at this stage that the child's character begins to take shape. What a child shows in the romantic stage of adolescence determines how his future life will be shaped and enriched by ideals and imagination. Secondly, the comprehensive application ability is acquired with the mastery of oral and reading ability. Compared with the whole cycle of infancy, the stage of comprehensive application ability is very short, because romantic elements are scarce in infancy. As far as the word "knowledge" is concerned, no matter how to explain it, children's initial understanding of the world begins after the end of the first cycle, and then enters an unparalleled romantic stage. Various concepts, facts, relationships, stories, history, possibilities, artistry and so on. With the language, sound, shape and color flooding into children's lives, it stimulates his feelings, stimulates his appreciation and inspires him to do similar activities. Sadly, however, in this golden age, children unfortunately fell in the shadow of teachers in cramming education. The period I am talking about is about four years. Generally speaking, they are between the ages of eight and twelve or thirteen. During this period, children's society has used their mother tongue and learned to observe and deal with problems with their mastered abilities. Babies can't cope with their surroundings, but children can; Babies can't observe it, but children can; Babies can't retain their mental activities through memory, but children can. Thus, the children entered a brand-new world. Of course, the precise stage prolongs itself by repeating itself in smaller cycles, which forms a whirlpool in the important romantic stage. Improving the ability of writing, spelling and calculation, and mastering a series of simple facts (such as successive British kings) are the basic contents of the precise stage. All these are necessary to train children's concentration and acquire knowledge. However, these things are fragmented in nature (page 32). More importantly, in the romantic stage, only it can push children into spiritual life like an unstoppable torrent. The success of Montessori's education method lies in its recognition of the leading role of romance in children's intellectual development. If this explanation holds, it also means the practical limitations of this method. To some extent, this kind of education is essential for all romantic education. Its essence is to attract tourists in the knowledge kingdom and stimulate bold and vivid innovation, but it lacks the necessary constraints and restraint in the precise stage.

Romantic stage, precise stage and comprehensive application stage form a big cycle. At the same time, the big cycle also includes small cycles. For example, learning to speak in infancy has formed a small cycle. Small circulation promotes the progress and development of large circulation.

Mastering the language When the child's intellectual development begins to approach the end of the romantic stage, this cyclical growth process makes him tend to learn accurate knowledge, and language naturally becomes the main content of his study. This is an expression that he is quite familiar with. He learned some stories, history and poems describing the life of other people and other civilized societies. So from the age of 1 1, he began to pay more attention to the acquisition of accurate knowledge. Finally, in the three years from 12 to 15 (page 33), you must enrich yourself with a lot of language content, so that if you go according to plan, you can get a definite result, which is worthwhile. I can guess that under these time constraints, we can properly focus on one place. We can say that at the end of this stage, children can master English, read very simple French fluently, and have completed the preliminary study of Latin; I mean, being able to master simple and accurate knowledge of Latin grammar and Latin sentence structure, reading some works suitable for Latin writers (these works may have been simplified, with the help of beautiful translations), and their reading and understanding of the original text can enable them to master all the contents of the original literature. In my opinion, the method of learning these three languages in this way is completely within the ability of ordinary children, as long as they are not distracted by other subjects that need accurate learning. Of course, some gifted children can learn better and go further. Learning Latin is not difficult for these children, so at the end of this stage, they can start learning Greek-if they have a hobby in literature and they will study for at least a few years in the future. In this timetable, other issues are in a secondary position, which means that we should adopt different attitudes. First of all, we should remember that these semi-literary subjects, such as history, will be integrated into language learning in the future. Without a little knowledge of European history, it is difficult to read literary works in English, French and Latin. I'm not saying that all specialized history teaching should be abandoned. However, I do suggest that this subject should be expressed by what I call "romantic spirit", and students should not take a large number of systematic exams that require accurate memory of details. In this period of development, science should be in its romantic stage. Students should observe the experiment by themselves, and only require accurate local thinking. Whether interested in scientific theory or for technical purposes, the essence of the importance of science is to apply science to specific objects. (Page 34) Every such application will lead to a new research topic. Therefore, all scientific training should start with research and end with research, and we should grasp the factual materials that occur in nature from beginning to end. The limitations of correct guiding methods and experiments suitable for this age depend on rich experience or not. But I still appeal that this period is very suitable for romanticism to study science. By the time the focus of science reaches 15 years old, the precise stage of language and the romantic stage of science have come to an end, followed by the comprehensive application stage of language and the precise stage of science. This is a short period, but it is crucial. I think this period is about one year, which will undoubtedly change the balance between the previous courses. In this period, it is necessary to concentrate on scientific study and pay less attention to linguistics courses. Follow the romantic stage of science and focus on science for one year, so that students can deeply understand the important principles that determine the development of machinery, physics, chemistry, algebra and geometry. Understanding these does not mean starting to study these courses, but integrating the knowledge learned before by systematically expounding the concepts of these disciplines. Take algebra and geometry for example. I take them as examples because I know something about them. In the previous three years, students have learned to use simple algebraic formulas and geometric principles to solve measurement problems or other scientific work about calculation. In this way, by emphasizing the expression of correct results with numbers, students' arithmetic ability is strengthened, and they are also familiar with the formula of letter expression, the concept of geometric proposition and other simple methods to deal with problems. In this way, we won't waste a lot of time in the process of getting familiar with scientific concepts. The students are going to learn some algebraic and geometric principles that they should thoroughly understand. In addition, in the previous stage, some boys showed a certain talent in mathematics, and they will continue to develop in this respect. In the last year, they strengthened their mathematics at the expense of other subjects. I just take math as an example. At the same time, language circulation is in the stage of comprehensive application. At this stage, the accurate study of grammar and composition has come to an end temporarily, and language learning is limited to the reading of literary works, focusing on the ideas of works and their general historical background; The time allocated for historical research will be shifted to a short period of precise research. This period is chosen to accurately explain what happened in this important era, and also to show how to judge the people and policies concerned more simply. At this point, I have probably made a general outline description of the education from infancy to sixteen and a half years old, which is arranged according to the pace of life. It is feasible to carry out general education in this way, which is helpful for students to concentrate on their studies and maintain their vitality. Therefore, accuracy often describes a subject that has been understood but needs urgent treatment. Each student will focus on different subjects in turn and find out his own interests. Finally-this is the one I cherish most among all the goals-science students can get a rare literature education and start to form the habit of thinking independently in the scientific field at the most sensitive age. After sixteen, new problems began to appear again. The study of scientific knowledge of liberal arts students has reached the stage of comprehensive application, and most of them explain the main achievements and general ideas of science in the form of lectures. A new round of language, literature and history study has begun. But it is no longer necessary to know more details. For learners of scientific knowledge, the precise stage will last until the end of middle school, during which students will deepen their understanding of broader scientific concepts. But at this stage of education, the problem is very individual, or at least (page 36) it can be broken down into many cases, so that there is no universal method, but I strongly recommend that all learners continue to learn French, and if they have not mastered German, they should start learning German. University education If you can still stand my speech, then I want to talk to you about the importance of those ideas about university education. The whole growth stage from baby to adult has formed a huge cycle. The romantic stage covers the children's first twelve years of study and life, the precise stage includes the whole secondary school education, and the comprehensive application stage is from juvenile to adult. For those who want to continue to receive formal education after secondary education, university courses or courses equivalent to university level are very important comprehensive application stages, and the spirit and concept of comprehensive application occupy a dominant position. University lectures are aimed at those who are already familiar with the details and processes, that is to say, at least they are quite consistent with previous training, so they are easy to master. In middle school, a student is bent over his desk to concentrate on his studies, while in college, he should stand up and look around. Because of this, it is a fatal mistake for students to waste their first year of college on reviewing what they have learned before with old ideas. In middle school, students have learned to understand general concepts from concrete and special examples through hard work; In college, he must learn to change from general concepts to concrete examples. A well-designed university curriculum is a comprehensive study of general laws. I don't mean divorced from specific facts, but to study specific cases to illustrate general concepts. The cultivation of intelligence is an aspect of university education, which pays attention to the combination of theoretical interest and practical utility-no matter what details you instill in a student, (page 37) the chances of encountering this detail in his later life are slim; Even if he did meet him, he might have forgotten what you taught him. Really useful education is to let students thoroughly understand some general principles, which can be applied to various specific details. In the subsequent practice, people may have forgotten the specific details, but their subconscious judgment will help them apply these principles to the immediate situation at that time. When you throw away your textbooks, burn your class notes and forget the details of the exam recitation, your study will be useful to you. The details you need are as obvious as the sun and the moon overhead; What you need occasionally can be found in any reference materials. The function of the university is to let you get rid of the details and keep the principle. When I talk about the principle, I can't even describe it in simple language. A principle really immersed in your bones is not so much a formal language expression as a habit of thinking. This kind of thinking habit has become the brain's response to some appropriate stimuli, which is reflected in some illustrative situations. When no one faces a situation, what he has learned will appear clearly and consciously in front of him. The cultivation of intelligence is nothing more than that when a person carries out an activity, his brain operates in a satisfactory way. Learning is often compared to such a thing: we stare at the open pages of all the books we have read, and when the opportunity comes, we choose the right page and read it aloud to the world. Fortunately, the actual situation does not contradict the above immature ideas; Therefore, the opposition between pure knowledge and professional achievement should not be as serious as we look at this problem with the wrong educational concept, but obviously much lighter. I explain my point of view in another way. The ideal of a university is not knowledge, but strength. The duty of a university is to turn children's knowledge into adults' strength. (Page 38) The Rhythmic Characteristics of Intellectual Development I will end my speech with the following two comments, which I hope to clarify by warning. The focus of this speech is the rhythmic characteristics of intellectual development. Man's inner spiritual life is a net made up of many strings. These threads will not be woven and extended together according to a unified standard. I tried to illustrate this truth with facts. I have observed some children with medium qualifications, who grew up in a smooth environment and developed their abilities normally. Maybe I misinterpreted this normal phenomenon. I have a good chance of failure; Because the evidence used to prove this is very difficult and complicated. However, don't be biased against the point I emphasize here because of any failure in one aspect. The process of intellectual development presents a rhythm, which contains an intertwined cycle. As a small vortex in development, the whole process is controlled by a more important cycle with the same characteristics. Moreover, this rhythm shows a universal law that is effective and reliable for most students, and the quality of our education must adapt to the corresponding stage of students' intellectual development rhythm. The problem of curriculum setting is not only a series of subjects, but all subjects should essentially start from the embryonic stage of intellectual development. The really important order is the natural order that should be recognized in the process of education.

"Intellectual development is rhythmic", which shows a universal law that is effective and reliable for most students. The quality of our education must adapt to the corresponding stage of students' intellectual development rhythm. Therefore, "we adjust the quality of education by adapting to the corresponding stages of students' intellectual development".

My second warning is: don't exaggerate the huge differences between the three different stages in a cycle. I suspect that when you hear the details of the three different stages of this cycle, many of you will tell yourself how much mathematicians like to make such a formal classification. I assure you, this has nothing to do with mathematicians, but the incompetence of textbooks made me make the mistake I am telling you now. Of course, I mean the difference in emphasis and main characteristics-romance, accuracy and comprehensive application, which exists from beginning to end. But it dominates alternately, and this alternation forms different cycle periods. (page 39)

After reading the whole chapter, we can see the romantic feelings of the author as an educator. His interpretation ranges from problems to viewpoints, from theory to practice, from scientific principles to life growth.