The advanced and scientific management of intangible mathematics determines that Montessori should use the same principle in all educational contents for children. The contents of education include: daily life practice, activities before mathematics, sensory education, mathematics education, language and Chinese education. Cultural education, history education, geography education, animal and plant education, astronomy education, science education, music education and painting education. From then on, let children use a principle method to enter the operation and learning of various courses.
Such an advanced educational method closely links the development of children's education, the preparation of teachers to serve children and the strict setting of educational environment like an invisible chain in a rigorous, accurate, standardized and scientific way.
When children enter the environment, any operation and study will bring them a match between people and things to discover the principle of teaching AIDS. Just like people use mobile phones. Children enter the state of education through concretization and transparency every day, and there is a process of integration, continuation, repetition and detail.
On Montessori classroom education.
All the educational contents in the classroom use specific teaching AIDS, and children are given the right to choose freely, so that children's nature, because of freedom, will spontaneously and continuously operate countless teaching AIDS on the teaching aid rack. This has nothing to do with the traditional education model that all of us have experienced. Learning the number 1- 10 is not taught by the teacher, but matched with Montessori's working principle. Because the amount given to the child is 1-55, the child will match several amounts according to the numbers. This kind of educational method, which allows children to recognize knowledge numbers through experiments, allows children aged four to five to choose continuous input. Children's academic achievements don't need to remember 1- 10 immediately and enter the calculation, but pay attention to and apply it to new educational content and self-discovery learning. Today, a child entered the cognitive learning of 1- 10. In fact, sometimes several children are also learning. The way to learn is to observe the hands-on children to operate, just like someone watching chess in the street. Children who can enter observation actually gain a cognitive experience. This kind of experience is called "infiltration" in class. It is also a transparent learning process for children, which is presented by children themselves, just as a teacher teaches all children to sit on the blackboard and watch him write a Chinese character "Da" for children to see. But that kind of watching is a dynamic educational model.
A child's operation is a transparent psychological experience for specific teaching AIDS. In fact, many children enter this kind of experience with children's observation through transparency. Children can enter observation, indicating that children are calm as water and automatically absorb the experience of growth and discovery in calm. In view of this environment in which children learn from each other, the situation is that children are teachers among children and also their own teachers. This "teacher" is the continuous learning that the product brings to them. Let children grow up, from beginning to end, into a kind of independent learning, independent discovery and independent creation.
Giving children this constant psychological "transparent" experience, Montessori sets all educational products as a whole theme, aiming at developing children's wisdom from the source. Integration will bring children an overall understanding of things. In the form of curriculum, teaching AIDS run through educational activities with educational content as the theme.
History education, knowing time. From knowing clocks and watches, one second, one minute, one hour and twenty-four hours a day, children can find that time is a string of numbers by operating teaching AIDS. Re-understand what people's daily activities, items and work progress are seven days a week, and children find that educational content and relationships are related. There are four seasons for social activities on January 30, and each season has something to do with people's lives. The four seasons are twelve months. What festivals are there in twelve months? It also makes children feel that time is flowing, accompanied by various human activities.
Montessori's educational products are mainly made by sets, so it has formed a large number of characteristics for children. Enough can make children interested in constant touching, which is like a child playing with sand in the yard, far less than going to the beach to make children have fun. Children get into the habit of silence, concentration, patience and persistent doing things by themselves through touch. The children gradually entered the theme education, which brought them consistent working principles. Because of persistent cognition, they have persistent discoveries in persistence, and because of persistent discoveries, their intelligence has been continuously improved.
Give this kind of holistic education, so that children can have a continuous learning.
One day, I found that a child had no parents to pick him up after school. He was alone with a teaching aid on the carpet in the classroom. I found that my child carried six sets, the number of which exceeded 1 10, and the child carried out joint operation. Joint operation is to operate multiple sets of teaching AIDS together, which is the best state for Montessori children to enter the operation and development. So I became interested in him. I trained him to sit aside, and he operated the teaching AIDS into various graphic patterns. However, the operation is always carried out in the order set by the teaching aid. He made me feel that the sequence of actions is not simply like many children looking for a sequence, but using the principle of thinking and building a tower-shaped house with complete sets of teaching AIDS, no! It should be said that it is a tower-shaped frame model built in sequence. I believe that an architect with a discerning eye will definitely bring him creative inspiration. It reminded me of the first time I went to Beijing Tiantan Park. The pattern of the top of the Great Hall in the Temple of Heaven is hexagonal with tens of meters of wood. All the wood is from long to short, from the first floor to the seventh floor, to the top of the last floor, in a tower shape. I didn't understand the principle used by the ancients at that time. Because of its strangeness and grandeur, I still clearly remember it on the cultural relic card in the hall. "There are no nails in this hall, and the connections between the timber are riveted."
This child has entered such a state that I believe that he has developed his inner thinking into rigor and meticulousness through a series of actions. He has a unique conception, thinking while building, and completed this great creation like a superb craftsman. I am as excited as that child. Then, I hurried to the office to get a camera and took it. Four years later, I went to a Montessori kindergarten in Beijing to give a lecture. From the window of the kindergarten, I also saw a photo exactly like the one I took at that time. I think children's discoveries are all made by the same principle and method, which makes children's discoveries different. It is said that the tower frame model built with six sets of teaching AIDS was first discovered by several children in Taiwan Province Province.
Later, I asked my children to draw the results of the operation into a sequence diagram. At this time, our garden's teaching requirements for teachers to enter the Montessori operation class can be drawn as having a sense of space for objects, which is extremely effective for teachers to accurately observe children in classroom teaching. Because painting depends on the result of thinking, it can't be drawn because it is not recognized. This method for children can quickly promote children to learn mathematics through painting. This is a new main learning content of step-controlled mathematics primary school edition. The child said it was graphic mathematics.
The child drew all his operation forms into words. Later, I asked him to use numbers to calculate the total length of each number, and he actually deduced it quickly. This allowed me to find a basis for continuing to delay the setting of mathematics textbooks for children's primary schools in the future.
Using the principle of education, we can cultivate the entrance of children's surface order. After children form their ideas through the order established by mental actions, they will consciously abide by public order and good customs and strictly abide by the normative behavior produced by moral education established by mental order after entering the society. Children's thinking enters order, and order refers to order. Order refers to the accuracy and accuracy of countless items. That is, the result of countless thoughts. This is the highest development state of Montessori children. Children enter the serialization of thinking, enabling them to do things. They are more rational, smarter and more accurate in thinking and doing things, and at the same time, there is a potential burst of creativity.
Principle education will make a mixed-age education constantly position education through principle. Every time I give a lecture, I ask what I talk about the most. Mixed-age classes allow children to choose operation and study freely. How to take this course? This is also the same puzzle when I came into contact with Montessori education. When I first attended the Montessori education class, I was surprised to find that the children obeyed the order of the class very much because they had something for them to operate. I wanted to cry that day.
It was not until one year after Montessori education was implemented that I found more and more that the classroom was a circle to link children to the environment prepared by adults for children. As long as teachers and children don't go out of the circle, the principle in educational products is like that each of us wants to eat in a fast food restaurant and consciously enters a fixed dining seat in the fast food restaurant. Therefore, people who want to eat must observe the fixed seats and control people in a fixed order.
This "fixed seat" is set by educational products, so that the following can achieve the unity of the three.
First, the contents of educational products are set according to the principle of unity.
Second, as long as children abide by the three elements of the environment and give them the right to operate freely, children will naturally discover the principle of educational product setting, enter control errors and correct them (see control errors 1).
Third, by giving children the above two rights to respect children's personality development and freely choose their jobs, teachers have virtually achieved the goal of controlling adults' education to children with the principle of teaching AIDS.
In order to control teachers' enlightenment to children, Montessori used a unified three-stage education prompt. Let the teacher lead the children into the first cognitive learning activities of all teaching AIDS. For example, learning about red.
The first stage: the combination of feelings and names. Say to the child, "This is red."
The second stage: know the object with the corresponding name and say "give me the red one" to the child.
The third stage: remember the names of the corresponding items. We showed a child an object and asked him, "What color is this?" . The child replied, "This is red".
There is also the function of each teaching aid product, which is only set to let children discover a concept. Once the teacher gives the child a hint, but the child has not developed to the point of discovering it, it completely steals the concept that belongs to the child's cognition. Children can't find the face match immediately when they are learning geometric three-dimensional operation, even after many operations. Every time you just enter the game, the teacher can't correct it or disturb it unless the child asks you for help, even if the teacher unconsciously tells him. The purpose of controlling the teacher not to educate the child is to let the child enter a repeated operation, and the child will eventually find out for himself.
Identifying the entrance of a teacher's works with sensory principles is the entrance of a child's development works. Whether the child's development is good or not is reflected in the teacher's preparation for the child. Just like when we do something, the more fully prepared you are, the better the result will be, which is mainly reflected in the careful teaching of teachers.
The teacher gave the children a group tactile exercise class, which was about feeling the temperature difference. The teacher first filled four identical bottles with water in one container, and then adjusted the temperature difference of the four identical containers with a thermometer, which was equivalent to putting Montessori's educational principles in. When a child touches it, it feels from cold to hot. Just like a child finds that a long stick becomes shorter. If the teacher does not use a thermometer to adjust the temperature, but casually checks the temperature of the water according to his own feelings in the container, it will not be able to accurately penetrate Montessori's educational principles, and because of the teacher's mistakes, it will also bring the wrong contact feelings to the children. Feeling from cold to hot through the container actually reflects a mathematical warming process through the temperature of water. The teacher wants the children to feel the accuracy of this process, and the principle also requires the teacher to input the detailed process of preparation every time. This detailed process is that after the teacher finishes this exercise for the children, he will adjust the water temperature every time like the first time to ensure that the children can practice alone.
Teachers enter the state of preparation through many details of Montessori's educational principles. Through the rigor, scientificity and digitalization of educational products in the environment, teachers are increasingly shaped into a rigorous, scientific and digital counterpart, so the authenticity, responsibility, detail and equivalence of children's services are also revealed. (Equivalence refers to an effect that people find a suitable product and change themselves. In the real practical sense, it is by no means empty talk to carry out Montessori's educational thought and call on all mankind to respect the growth of children and help the development of children's lives.
The great success of Montessori education lies in educating children with technical products and unified principles, which fundamentally ensures that children can enter, constantly explore and pursue the development of life, and constantly copy their own bodies by using the principles in the products themselves, and automatically enter self-education, so that children can develop their own lives, achieve themselves, observe order, learn from each other, help each other, cultivate norms and improve their living ability in a management that does not exclude learning human knowledge every day, but also allows children to simulate socialization. Teachers will become the object of education in a unique way, and they will be lasting and continuous service. This kind of education should be paid enough attention to by human education.
Montessori education promotes children's education to a systematic education project, and also endows people with education. As long as the principles and methods are followed, it will not deviate from the time when children learn human knowledge, but also improve their sense of responsibility to society and the development track of moral education. Because the three services of Montessori education to children (isolation, error control and indirectness of education) will play a role in connecting children to learn knowledge, cultivate children's conduct and standardize children's future social responsibility.
These three principles are more and more publicized, standardized and widely used by social management, but Montessori successfully applied them to educate children at the beginning of the twentieth century.
Traditional education must learn from it if it wants to enter substantive improvement and reform. Otherwise, this kind of reform will be futile.
And let me believe that as long as Montessori's educational principle and three service methods for educators are set in the education of primary school, junior high school and senior high school, the educational effect will be the same as that of children's development, even very good, because the advanced educational equipment and means are integrated now. Montessori's educational method has been successfully applied to American high school education.
Sequential mathematics is a comprehensive proof and analysis of the technical content of Montessori educational products by using Montessori educational principles. Educational experiments have proved that, firstly, due to the adoption of principled education, it only takes three years to learn mathematics in six years in primary school, and children can teach themselves; Second, it can improve children's interest in learning mathematics, let them enter the research of observation, thinking and exploration, and establish new self-confidence and autonomous learning. The new thinking established by using mathematics can be further developed and applied to other fields.