First, the principle of close contact with life
Real life is the source of children's mathematical concepts. Children's mathematical knowledge is closely related to their real life. It can be said that mathematics is everywhere in children's lives. Everything that children touch every day is related to number, quantity and shape. For example, when they say how old they are, they will involve numbers; Compared with the height of other children, it is actually a comparison of quantity; You will see different shapes when building blocks. Children will encounter all kinds of problems in life, which need to be solved by mathematics. For example, if a child wants to know how many people there are in the family, he needs to count them. When taking things, children always want to take "more" and "bigger", which requires distinguishing the quantitative relationship between more and less, big and small. In short, many problems in life can be solved by a math problem, which can be an opportunity for children to learn math.
On the other hand, judging from the characteristics of mathematical knowledge itself, many abstract mathematical concepts are difficult for children to understand without the help of concrete things. Real life provides children with a bridge of abstract mathematical knowledge. For example, some children can't understand the abstract meaning of addition and subtraction, but in fact they may often use addition and subtraction to solve problems in life, but they just don't connect this "mathematics in life" with "mathematics in school". If teachers don't teach children "from concept to concept", but contact their real life, with the help of their existing life experience, they can make these abstract mathematical concepts according to their familiar life experience. For example, letting children play shopping games in the game corner, and even inviting parents to take their children shopping, giving children the opportunity to calculate money and things by themselves can make children realize the application of abstract addition and subtraction operations in real life and help them understand these abstract mathematical concepts.
Mathematics education should be closely linked with the principle of life, which should be reflected in:
The content of mathematics education should be related to children's life, and the educational content should be selected from children's life. What we teach children should not be abstract mathematical knowledge, but should be closely related to their real life. For example, when teaching the knowledge of the composition of numbers, children can be introduced to divide things in their daily lives, so that they can be more familiar with and accept the concept of the composition of numbers.
Guide children to learn mathematics in life. In addition to planned and organized collective teaching, mathematics education should be carried out in children's daily life. For example, when dividing snacks, you can guide children to pay attention to how many snacks there are, how many children there are, how to divide them, and so on.
In addition, mathematics education should be linked with children's lives, guide children to use mathematics, and let children feel the application and role of mathematics as a tool in real life. For example, raising small animals in kindergartens can guide children to measure their growth. In game activities, you can also create a situation for children to use mathematics. For example, in shop games, children can learn to buy things and calculate the price of goods. These are actually hidden mathematics learning activities. Children often accumulate rich mathematical experience unconsciously. These experiences provide a broad foundation for them to learn mathematics knowledge.
Second, the principle of developing children's thinking structure
The principle of "developing children's thinking structure" means that mathematics education should not only focus on the teaching of specific mathematical knowledge and skills, but also point to the development of children's thinking structure.
According to Piaget's theory, children's thinking is a whole structure, and the development of children's thinking is manifested in the development of thinking structure. Thinking structure is general and universal, which is the premise for children to learn any specific knowledge. For example, it is impossible for preschool children to arrange sticks of different lengths in a logical way when there is no abstract concept of sequence in their thinking structure. Conversely, children's learning process of mathematical concepts also contributes to the development of their general thinking structure. This is because mathematics knowledge has a strong logic and abstraction, and learning mathematics can exercise the logic and abstraction of children's thinking. In short, the process of children's construction of mathematical concepts is quite consistent with the construction of their thinking structure.
In children's mathematics education, children's mastery of some specific mathematics knowledge is only a superficial phenomenon, and the essence of development lies in whether children's thinking structure has changed. Take long and short sorting as an example. Some teachers teach children the "correct" sorting method: find the longest one at a time, and then find the longest one from the remaining sticks ... Children seem to be able to complete the sorting task correctly according to the method taught by teachers, but in fact they have not obtained the logical concept of order and their thinking structure has not been developed. What children really need is not to teach them sorting skills, but to fully operate and try, and get an opportunity to understand. Only in this way can they gain a logical experience from it and gradually establish a sequential logical concept. Once children have the necessary logical concepts, it is no longer difficult for them to master the corresponding mathematical knowledge.
In short, the acquisition of mathematical knowledge and the construction of thinking structure should be synchronized. In children's mathematics education, teachers should not only teach children mathematics knowledge, but also consider the development of children's thinking structure. Only when children's thinking structure is developed at the same time, their mathematical knowledge is the most solid and unforgettable knowledge. As a child said to Piaget, "Once you know, you will always know." (When Piaget asks a child who has reached a conservative understanding, "How do you know?" At that time, the children said the above sentence, which Piaget thought was a wonderful answer.
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In educational practice, teachers often need to choose between imparting mathematical knowledge and developing thinking structure. In fact, the relationship between the two is the relationship between specific interests and general interests, and the relationship between immediate interests and long-term interests. Sometimes, in order to give children more opportunities for self-adjustment and assimilation, teachers give up teaching some specific knowledge and skills, thus fundamentally changing children's way of thinking, which does not violate the purpose of mathematics education.
Third, let children operate and explore principles.
The principle of letting children operate and explore is to let children construct mathematical knowledge through their own activities. Mathematics knowledge is constructed by children themselves, and this construction process is also the process of building children's cognitive structure. If a teacher only pays attention to the achievement, and "teaches" a lot of children, it is actually depriving him of his own development opportunities. In fact, children's cognitive structure cannot be developed through unilateral "teaching", but must rely on their own interaction with the environment and develop in the interaction between subject and object.
In mathematics education, the interaction between subject and object is reflected in children's activities of manipulating material and exploring the relationship between things. Let children operate and fiddle with concrete objects, and urge them to internalize concrete actions in their minds. This is the fundamental way to develop children's thinking. Mathematical knowledge based on action is the most reliable knowledge that truly conforms to children's age characteristics and adapts to their cognitive structure. Proficiency achieved through memory or training does not have the value of developing thinking.
The principle of letting children operate and explore requires teachers to take operating activities as the main teaching method in practice, instead of letting children watch the teacher's demonstrations or intuitive pictures or listen to the teacher's explanations. Because operating activities can give children the opportunity to coordinate and understand the relationship between things at the specific action level, it is a learning method suitable for children's characteristics. Take the cognitive quantity of small class children as an example. Teaching children oral arithmetic can help them understand the order of numbers, but it can't help them understand the quantitative relationship. Many children in small classes can count a lot, but this does not mean that they really understand the quantitative relationship between the order of logarithm and the order of number. Through operating activities, children can not only count, but also coordinate oral calculation and counting, thus understanding the practical significance of counting.
Operation activities also provide a foundation for children to internalize mathematical concepts and understand the abstract meaning of numbers. On the basis of skilled operation, children can concentrate and internalize external actions, transform them into internal actions, and finally transform them into thinking in their minds. For example, when children's concept of number develops to a certain extent, they can count groups intuitively without counting points, and finally children can understand the number they represent when they see a certain number, but in fact these abilities are based on the initial operation activities. Therefore, arithmetic activities are very important for children to learn mathematics.
In addition, this principle also requires teachers to turn learning mathematics into a process of children's own active exploration, so that children can explore and discover mathematical relationships themselves and gain mathematical experience. The role of a teacher "teaching" is actually not to give children a knowledge result, but to provide them with a learning environment: an environment that interacts with materials and people. Of course, teachers themselves are part of the environment and can also interact with children, but they must interact with them equally at the level of children. Only in this kind of interaction can children get positive development.
Fourth, attach importance to the principle of individual differences.
The principle of attaching importance to individual differences is based on individual differences in children's development. It should be admitted that every child has its inherent uniqueness. This is not only reflected in everyone's unique development steps, rhythms and characteristics, but also in everyone's temper and attitude.
In mathematics education, children's individual differences are particularly obvious. This is not only because mathematics learning is a kind of "high-intensity" intellectual activity, which can fully reflect the difference of children's thinking development level, but also related to the characteristics of mathematics itself-mathematics is a strictly limited field, with a specific symbol system and rules of the game, and does not need as complicated life experiences as literature and other fields, so this talent is also easy to show. (Gardner, a contemporary psychologist who studies gifted children, also points out that mathematics, chess and music playing are the three fields that are most likely to produce young talents. )
The individual differences in children's learning mathematics are not only manifested in the differences of thinking development level and development speed, but also in the differences of learning methods. Even children with learning difficulties have different difficulties. Some children lack the ability of generalization and abstraction, while others lack learning experience.
As educators, we should take into account the individual differences of different children, so that each child can develop according to his own level, rather than the same requirements. For example, when providing children with operational activities, you can design activities with different levels and difficulties, so that children can freely choose activities that suit their own level and ability.
For children with learning difficulties, teachers should also analyze their specific situation and give different guidance according to different difficulties. For example, for children who lack the ability of generalization and abstraction, teachers can guide them to summarize and inspire them appropriately. For children who are inexperienced and lack summary materials, they can provide some opportunities for operation and practice to supplement their learning experience.